tag:blogger.com,1999:blog-42721056181793005002024-03-20T01:13:50.510-07:00Statistics to prove anything<center> "Oh, people can come up with statistics to prove anything, Kent. 14% of people know that."<br>
- Homer Simpson
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thoughts, examples, code, and anything else I find interesting regarding statistics. </center>Anonymoushttp://www.blogger.com/profile/02697157095904133223noreply@blogger.comBlogger9125tag:blogger.com,1999:blog-4272105618179300500.post-37648296543706138182014-01-01T13:39:00.000-08:002014-01-01T13:39:35.876-08:00Top Albums of 2013<h2>
<span style="font-family: Arial, Helvetica, sans-serif;">Top Albums of 2013</span></h2>
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<span style="font-family: Arial, Helvetica, sans-serif;">Background</span></h3>
<span style="font-family: Arial, Helvetica, sans-serif;">Spotify is pretty amazing - not the free version (I think I still prefer Pandora radio for that) - it has to be the paid version to really get the full effect. It has figuratively opened my mind to music that I never before would have considered (and some I will continue to deride). Although I still tend to stay within the confines of classic rock mixed with more modern indie and alternative rock, I have certainly explored and expanded more this past year than before. The biggest undertaking I accomplished was </span><span style="font-family: Arial, Helvetica, sans-serif;">listening to each of the 500 albums listed in the Rolling Stone's </span><a href="http://www.rollingstone.com/music/lists/500-greatest-albums-of-all-time-20120531" style="font-family: Arial, Helvetica, sans-serif;" target="_blank">500 Greatest Albums of All Time</a><span style="font-family: Arial, Helvetica, sans-serif;"> (the May 2012 updated list, many, but not all are available on Spotify). Although I don't have an exact count, I have listened to well over 600 albums this year. When I think about it, I don't know how many albums I listened to <i>before</i> this year, but it couldn't have been a ton more than that.</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">I decided to rank my favorite albums of 2013, and when I say rank, I mean it has to involve some form of measurement. I find it very difficult to make "top-<i>x</i> lists," and am often very critical of such lists. One thing that drives me crazy is when radio stations have marathons over some holiday weekend of the "top 100 songs of all time, as voted by you, the listener!" When it is actually "We let you, the listener, go to our website and pick 5 songs from our catalog (I'm not sure who actually does this, but it couldn't possibly be representative of the actual listening audience, or am I wrong?), which is limited to 'classic' rock of the 60s, 70s, and maybe 80s." You then end up with weird things like Boz Scaggs' "Lido Shuffle" being ranked higher than Fleetwood Mac's "Go Your Own Way." </span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">While I can't promise that I won't have infuriating choices, I can at least be upfront about the rules I am playing by. Rules which are: </span><span style="font-family: Arial, Helvetica, sans-serif;">I am limiting my list to the top albums of 2013 that I personally have listened to at least twice (with one exception). There are a couple albums that in doing my research for 2013 that I decided to give a listen to, but they left imprints on my ears too late in the game to be included. That's really about it, If I don't discuss an album from 2013 that should be on this list, you can safely assume I simply haven't come across it yet. </span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">Creating the list</span></h3>
<span style="font-family: Arial, Helvetica, sans-serif;">I started by listing all the albums I could remember having listened to over the past year, and followed it up by looking up </span><a href="http://en.wikipedia.org/wiki/List_of_2013_albums" style="font-family: Arial, Helvetica, sans-serif;" target="_blank">albums released in 2013</a><span style="font-family: Arial, Helvetica, sans-serif;"> (</span><span style="font-family: Arial, Helvetica, sans-serif;">A quick side note - Buckethead released released 33 albums in 2013! ...and I didn't listen to a single one). After compiling the list I had about 20 albums that I had listened to extensively, which doesn't seem like a ton. I probably am not really qualified to write a "top list of" like you would read on a reputable website, but we can carry on understanding the shortcomings of the rules I set.</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">Now that I have a list, I need to find the appropriate order. It is tempting to create some model involving metrics like number of times I listened to each album, number of sales, chart ranking, twitter mentions, Metacritic rankings, etc. Creating such a model really wouldn't get at the heart of what I really want to accomplish. </span><span style="font-family: Arial, Helvetica, sans-serif;">While music preference is very much a personal subjective matter, I can certainly objectively say that I'd rather listen to one album over another. Of course my preference might change over time, and others will certainly have their own opinions, I hope to give a snapshot of what I connected with this past year, and what I think others might appreciate.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span><span style="font-family: Arial, Helvetica, sans-serif;">After compiling my list, in order to calculate rankings I first randomly ordered the albums and then created a grid with a row and corresponding column for each album. I then compared each row album to each column album and asked myself "which album would I rather listen to?" Of course if I am in a mood to dance I might choose something different than when I am feeling a bit existential, so I try to imagine that I'm in a neutral mood, and haven't listened to either album recently. Here's my grid:</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">Results</span></h3>
<span style="font-family: Arial, Helvetica, sans-serif;">Ordering the data by rank results in the following ranking. We'll go with the top 10 (even if it is an arbitrary number - why not top 8 or 11? I suppose its important to support the metric system) </span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">Two quick notes</span></h4>
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<li><span style="font-family: Arial, Helvetica, sans-serif;">I only listened to Yeezus once and included it so that every album I do like would get at least one vote. I listened to some of Kanye's other albums that are on the RS's 500 Greatest Albums, and I just didn't get them. This album in my estimation probably ranks much higher than </span><i style="font-family: Arial, Helvetica, sans-serif;">College Dropout</i><span style="font-family: Arial, Helvetica, sans-serif;">, but </span><i style="font-family: Arial, Helvetica, sans-serif;">Late Registration</i><span style="font-family: Arial, Helvetica, sans-serif;"> </span><span style="font-family: Arial, Helvetica, sans-serif;">is more listenable.</span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;">I guess I'm not entirely consistent, as evidenced by the several ties. For example, I have <i>AM</i> over both <i>Comedown Machine </i>and <i>Modern Vampires of the City</i>, both of which are over <i>Evil Friends</i>; yet I put <i>Evil Friends</i> over <i>AM</i></span><span style="font-family: Arial, Helvetica, sans-serif;">:</span></li>
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<span style="font-family: Arial, Helvetica, sans-serif;">The Omissions</span></h3>
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<li><span style="font-family: Arial, Helvetica, sans-serif;"><b>Paul McCartney - </b><i style="font-weight: bold;">New</i> perhaps his best effort since <i>Chaos and Creation in the Backyard</i>, but his worst named album since <i>Kisses on the Bottom</i> </span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;"><b>Deerhunter - </b><i style="font-weight: bold;">Monomania</i> Would have made it higher on the list if I had heard the album earlier</span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;"><b>Elvis Costello and The Roots - </b><i><b>Wise Up Ghos</b></i><b><i>t</i></b> Wasn't a fan, I really didn't like a lot of Costello's stuff in the RS's 500 either.</span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;">Many other, I'm sure</span></li>
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<span style="font-family: Arial, Helvetica, sans-serif;">The other not top 10ers</span></h3>
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<li><span style="font-family: Arial, Helvetica, sans-serif;"><b>Franz Ferdinand - <i>Right Thoughts, Right Words, Right Action</i></b> The lead single might be the weakest song on the album, otherwise it is what I've come to expect from a Franz Ferdinand effort</span></li>
<li><b style="font-family: Arial, Helvetica, sans-serif;">Daft Punk - <i>Random Access Memories</i></b><span style="font-family: Arial, Helvetica, sans-serif;"> This was just a great album, just happens to be outside of what I usually listen to</span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;"><b>New Politics - <i>A Bad Girl in Harlem</i></b> Fun album with some very catchy tunes</span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;"><b>David Bowie - <i>The Next Day</i></b> I can't say enough about Bowie. Its no <i>Station to Station</i>, but a great listen</span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;"><b>Deafhaven - <i>Sunbather</i></b> This was a pretty great album for a style I don't listen to as much. Very beautiful amongst the metal. This one is definitely worth a listen</span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;"><b>Pearl Jam - <i>Lightning Bolt</i></b> The ukulele touch on some songs is nice - I enjoyed Vedder's ukulele solo album. I haven't really listened to Pearl Jam much into the aughts</span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;"><b>Phoenix - <i>Bankrupt!</i></b> Some nice tracks and still interesting</span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;"><b>Dream Theater - <i>Dream Theater</i></b> Its always a good idea to wait 12 albums before releasing an eponymous album. I really loved <i>Octavarium</i> and <i>Metropolis Pt. 2: Scenes from a Memory</i>, but haven't been as impressed with their other albums</span></li>
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<span style="font-family: Arial, Helvetica, sans-serif;">My Top 10</span></h3>
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<span style="font-family: Arial, Helvetica, sans-serif;">10. The Flaming Lips - <i>The Terror</i></span></h4>
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<span style="font-family: Arial, Helvetica, sans-serif;">The Flaming Lips are one of those bands that I would hear a song of theris here or there over the years, but I didn't really fully appreciate them until earlier this year. <i>Yoshimi Battles the Pink Robots</i> might be their magnum opus, but this simply is a beautiful album. Existential lyrics with haunting psychadelic landscapes reminiscent of some early Pink Floyd. This album wasn't written to release singles, but rather is a work of art as a whole.</span></div>
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9. My Bloody Valentine - <i>m b v</i></span></h4>
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<span style="font-family: Arial, Helvetica, sans-serif;">I listened to the album <i>Loveless</i> as part of the RS 500 albums, and at that time I thought that it was a great album, if only I could hear through all that distortion. But what without the distortion, what would be the point? After the second track, "Only Tomorrow," I was hooked. A beautiful album that, in my opinion, surpasses its predecessor</span></div>
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8. Foxygen - <i>We Are the 21st Century Ambassadors of Peace & Magic</i></h4>
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One of those albums that I kept seeing critics praise, to which I add my own. I have listened to my fair share of The Beatles, both in and out of their experimental phase, but there really isn't a lot of psychedelic rock that gets played on classic rock/oldies stations. It wasn't until I heard more of The Kinks, Jefferson Airplane, among others, that I really gained an appreciation for that sound, and this is a great album for anyone looking to combine modern indie rock with those psychedelic influences. The influences, however, aren't limited to the San Franciscan sound, but also include the likes of The Rolling Stones and The Velvet Underground, almost as if a snapshot of those bands in the late 60s was being channeled. At times the album is humorous, at others pensive, but never lacking of interest.</div>
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<span style="font-family: Arial, Helvetica, sans-serif;">7. Queens of the Stone Age - <i>...Like Clockwork</i></span></h4>
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<span style="font-family: Arial, Helvetica, sans-serif;">It took a few listens before I loved <i>Songs for the Deaf</i>; I enjoyed this one on the first listen. Certainly their best album since <i>Songs for the Deaf</i>, with the lead single "My God is the Sun," being fairly representative of what to expect from the album. I'd list one of my favorite tracks as "If I Had a Tail," which despite discussing some pretty heavy themes, I can't help but find it humorous that Alex Turner of The Arctic Monkeys appears on the track (because monkeys have tails...)</span></div>
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6. Arcade Fire - <i>Reflektor</i></span></h4>
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<span style="font-family: Arial, Helvetica, sans-serif;">Perhaps the biggest disappointment of all albums released in 2013, if only because of the lofty expectations. Of course that is an exaggerated statement, but I was disappointed, even though it is a great album from a great band. We already had Daft Punk writing music that made us simultaneously want to ponder our existence and get down and dance, and Franz Ferdinand fills the void of indie club rock. Whatever, it isn't up to me to dictate the direction Win Butler and co. should take. I would rate Funeral as one of my all-time favorites, while Neon Bible and The Suburbs are amazing in their own right. I do love the "Black Orpheus" references of the album, and anything with David Bowie (even for just one song) isn't bad.</span><br />
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5. Cage the Elephant - <i>Melophobia</i></span></h4>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxm3oKxGAz96nWcTxn3LbQ_W_L4mWoKABORR2LaOxDKsU1eMuAfuJ0KoxaMiEz7Tp1bbQH1rxzmT8FpjCintoG175G9UaQZ6RAhJJtE9kVVkxjQ-z2dtJjJxXWiRB6R844LZDVYCer1cs/s1600/melophobia.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxm3oKxGAz96nWcTxn3LbQ_W_L4mWoKABORR2LaOxDKsU1eMuAfuJ0KoxaMiEz7Tp1bbQH1rxzmT8FpjCintoG175G9UaQZ6RAhJJtE9kVVkxjQ-z2dtJjJxXWiRB6R844LZDVYCer1cs/s1600/melophobia.jpg" /></a></div>
<div>
I looked up this album after having heard the single "Come a Little Closer" on the radio. I did enjoy their first two efforts, but I would have placed Cage The Elephant a bit behind The Black Keys and whatever Jack White is working on. I really enjoyed the album, and have kept going back to it since the initial listen. The bookend tracks provide a perfect intro and resolution to the album, while between is full of great blues tinged alternative rock.<br />
<br /></div>
</div>
<h4>
4. Portugal. The Man - <i>Evil Friends</i></h4>
<div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRJvTnUJZipE9ULThdtjAv5DWIA9eNLazTZYIJy3IPHmMvjzLyVX1sF2uzyY79h7GeKq4bu4kRFLdP-kJmbxay6eX6BYoPn1U2y7yZQboqMAu_JBQRWWnpn9AB-QsuLZTdek7xYIyHVxI/s1600/Evil+Friends.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRJvTnUJZipE9ULThdtjAv5DWIA9eNLazTZYIJy3IPHmMvjzLyVX1sF2uzyY79h7GeKq4bu4kRFLdP-kJmbxay6eX6BYoPn1U2y7yZQboqMAu_JBQRWWnpn9AB-QsuLZTdek7xYIyHVxI/s1600/Evil+Friends.jpg" /></a></div>
<div>
Another album that I looked up after hearing the lead single, "Purple Yellow Red and Blue." Sometimes there is just something about an album that just clicks; that you connect to on some deeper level. This was one of those albums. Danger Mouse just brings a great sound to alternative rock (psychedelic rock?), and has now produced a large number of albums that I love. Every time I listen to the album different tracks stand out, but then I realized that their song "Evil Friends" was used in a commercial currently airing, which might explain the strange desire I had the other day to visit and try their black bean and rice burritos.</div>
</div>
<div class="separator" style="clear: both; text-align: center;">
<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.youtube.com/embed/y61fLD0NWAA?feature=player_embedded' frameborder='0'></iframe></div>
<div>
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<h4>
3. The Strokes - <i>Comedown Machine</i></h4>
<div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcn_-NlnBI3qSoakpunLbjhbtSuui5_0QQqs9b4jXjgi52iQ4A0YiOXChbJgLh26_9NU7qItuwsXYB74JRKt_lqmIPLjBVkw97UsOuk69Fv-gYZkVWsBJEHVszvh9rUFgIK8VVCRcqbD8/s1600/Comedown+Machine.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcn_-NlnBI3qSoakpunLbjhbtSuui5_0QQqs9b4jXjgi52iQ4A0YiOXChbJgLh26_9NU7qItuwsXYB74JRKt_lqmIPLjBVkw97UsOuk69Fv-gYZkVWsBJEHVszvh9rUFgIK8VVCRcqbD8/s1600/Comedown+Machine.jpg" /></a></div>
<div>
Before this album came out, I read some rumors that it might be their last. It appears that may not be the case, as they are supposedly talking about doing a tour next year. The album is not held in high regard by the critics (see below); perhaps another one of those bands whose debut is transcendent or something, resulting in subsequent releases being panned if they are simply a continuation of the debut, or derided if they venture too far from what worked. The career arc of The Strokes is an interesting one, and if you were to jump from listening to <i>Is This It?</i> to <i>Comedown Machine</i> it would be quite a surprising leap indeed. I however have listened to this album countless times, and it just might be my favorite of theirs. The synthesizer worked for The Who on <i>Who's Next</i>, and it works here. filler, "Call It Fate, Call It Karma" is about as great of an ending an album could hope for.</div>
</div>
<div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgo2FKG2QntKemvvmPEa1AiRXedutHWo0rq-THegJ5JXV0vmKwjpT-EGfaHEnCYHwZkEJyFl1DugSFIxG8XPkNH-SkFiDTGTe2nvvvNaJFgEskaakI9uAlMw9AadWcb7AnNlEG1IGAYIuM/s1600/strokes_arc.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgo2FKG2QntKemvvmPEa1AiRXedutHWo0rq-THegJ5JXV0vmKwjpT-EGfaHEnCYHwZkEJyFl1DugSFIxG8XPkNH-SkFiDTGTe2nvvvNaJFgEskaakI9uAlMw9AadWcb7AnNlEG1IGAYIuM/s1600/strokes_arc.png" /></a></div>
</div>
</span><br />
<h4>
<span style="font-family: Arial, Helvetica, sans-serif;"> 2. Arctic Monkeys - <i>AM</i></span></h4>
<div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiOhFc-mzp-HSNZld0uX8iKA0w6-Rd1RJHTXn9ctMp8VVlT2hrToZTjxnI1B4Vftg0aB0-rA68j8sBjc4tQqnvdyzOD9A5wpRwHCBChXaxL3yn2Km0NmUXi3d_rdYVTofKZLdARsw0O3_s/s1600/AM.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiOhFc-mzp-HSNZld0uX8iKA0w6-Rd1RJHTXn9ctMp8VVlT2hrToZTjxnI1B4Vftg0aB0-rA68j8sBjc4tQqnvdyzOD9A5wpRwHCBChXaxL3yn2Km0NmUXi3d_rdYVTofKZLdARsw0O3_s/s1600/AM.jpg" /></a></div>
<div style="font-family: Arial, Helvetica, sans-serif;">
The Arctic Monkeys won me over years ago, and like Arcade Fire's <i>Reflektor</i> I anxiously awaited its release. This album, however, did not disappoint. I love the trademark sound of The Arcitc Monkeys - not just what you tend to hear on the singles of past, but the darker sound - not unlike what you hear on the lead single "Do I Wanna Know" (or the convenient theory confirming recently released B-side "You're So Dark"). This album embraces that feel, and it simply works. Their past two albums had their moments, and though they are in my regular listening rotation, this one is on par with <i>Favourite Worst Nightmare </i>and <i>Whatever People Say I Am, That's What I'm Not</i>. This time Metacritic agrees with my assertion:<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQBOYTJfYQ_yYgWaqHk1GkfpwgvO6BH2AujQR8uPLiZ0a4Dh04h599v9MrEtZuneRhROFkpL2DliNB2aG53kULX0sTzVkc50ann8UfniKlNrxNJlDXyQ_9_sJXL0sxjrojijvXwaG306U/s1600/am_arc.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQBOYTJfYQ_yYgWaqHk1GkfpwgvO6BH2AujQR8uPLiZ0a4Dh04h599v9MrEtZuneRhROFkpL2DliNB2aG53kULX0sTzVkc50ann8UfniKlNrxNJlDXyQ_9_sJXL0sxjrojijvXwaG306U/s1600/am_arc.png" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
</div>
</div>
</div>
<h4>
<span style="font-family: Arial, Helvetica, sans-serif;">
1. Vampire Weekend - <i>Modern Vampires of the City</i></span></h4>
<span style="font-family: Arial, Helvetica, sans-serif;">
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<div class="separator" style="clear: both; text-align: center;">
<span style="font-family: Arial, Helvetica, sans-serif;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiuT6wnFcvlrIhmjLoaeu_W3TJ4qIKVNpitevc1WLKQYrNngwQOgYA75bOxMMRP1jilVEuvMZL_S-MP-aHrABqP7ckO_6EXUSC97X-p2rF3auFhVz3gPPM4LYAwTsC596YdbbKgPtKF_28/s1600/vampire.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiuT6wnFcvlrIhmjLoaeu_W3TJ4qIKVNpitevc1WLKQYrNngwQOgYA75bOxMMRP1jilVEuvMZL_S-MP-aHrABqP7ckO_6EXUSC97X-p2rF3auFhVz3gPPM4LYAwTsC596YdbbKgPtKF_28/s1600/vampire.jpg" /></a></span></div>
<div>
<span style="font-family: Arial, Helvetica, sans-serif;">Earlier this year listened to their eponymous debut quite a bit - but I didn't care as much for <i>Contra</i>. I think a lot of how we feel about music is a reflection of where we are in life when we first listen to it, and perhaps <i>Contra</i> simply did not relate well to me. <i>Modern Vampires of the City </i>hits the nail on the head. It not only was what I needed to hear, they removed some of the sound that I considered to be obnoxious (realizing that it was a part of their identity and was the differentiation between them and other indie rock). This is clearly a concept album with each track building on the last, yet it is still able to produce several great standalone singles. </span><span style="font-family: Arial, Helvetica, sans-serif;">I keep coming back to this album as it never disappoints.</span><br />
<h3>
<span style="font-family: Arial, Helvetica, sans-serif;">Final Thoughts</span></h3>
</div>
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<span style="font-family: Arial, Helvetica, sans-serif;">
</span>
<div>
<span style="font-family: Arial, Helvetica, sans-serif;">I do enjoy <a href="http://www.metacritic.com/" target="_blank">Metacritic</a>, I think it is an interesting way of combining and weighting reviews. If there is a way to measure the consensus opinion on something, it is likely the closest you can find right now. Sometimes its also nice to stray out of the consensus and find something that is personally meaningful. If it can be both, all the better</span><br />
<div class="separator" style="clear: both; text-align: center;">
<span style="font-family: Arial, Helvetica, sans-serif;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRC4x3VMcl8m34zP7PWfaBZN_FaqYl5wkYiqiywU4zxxacUocZUiPXf4TGlTojqpgx8sQah66eOzm2nYBLpccTdGodrTVRrbopXzjRjR9NrCxiqZaTX72QPdJTftiMdFiAc5yW608A97o/s1600/metacric10.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRC4x3VMcl8m34zP7PWfaBZN_FaqYl5wkYiqiywU4zxxacUocZUiPXf4TGlTojqpgx8sQah66eOzm2nYBLpccTdGodrTVRrbopXzjRjR9NrCxiqZaTX72QPdJTftiMdFiAc5yW608A97o/s1600/metacric10.png" /></a></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">If nothing else, it is certainly worthwhile to seek out new music. I do hope that there is something on this list that others haven't considered before that they will discover and enjoy.</span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
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Anonymoushttp://www.blogger.com/profile/02697157095904133223noreply@blogger.com2tag:blogger.com,1999:blog-4272105618179300500.post-47269216099714331812013-11-05T13:35:00.000-08:002013-11-06T09:48:27.254-08:00Spider Web Plots in R
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<body>
<p>**Edit** I found a similar plotting technique using <i>radarchart</i> from the <b>fmsb</b> package, found at <a href="http://artax.karlin.mff.cuni.cz/r-help/library/fmsb/html/radarchart.html">http://artax.karlin.mff.cuni.cz/r-help/library/fmsb/html/radarchart.html</a></p>
<br>
<p>Unless your brain works differently than mine, then polar coordinates aren't great for being precise in consuming and measuring data. Use bar charts, not pie charts, right angles! That being said, “spider plots” or “web plots” or whatever you want to call these charts, can succinctly summarize a lot of information, and are visually pleasing.</p>
<p>Here's a function to create this kind of plot.</p>
<pre><code class="r">
webplot = function(data, data.row = NULL, y.cols = NULL, main = NULL, add = F,
col = "red", lty = 1, scale = T) {
if (!is.matrix(data) & !is.data.frame(data))
stop("Requires matrix or data.frame")
if (is.null(y.cols))
y.cols = colnames(data)[sapply(data, is.numeric)]
if (sum(!sapply(data[, y.cols], is.numeric)) > 0) {
out = paste0("\"", colnames(data)[!sapply(data, is.numeric)], "\"",
collapse = ", ")
stop(paste0("All y.cols must be numeric\n", out, " are not numeric"))
}
if (is.null(data.row))
data.row = 1
if (is.character(data.row))
if (data.row %in% rownames(data)) {
data.row = which(rownames(data) == data.row)
} else {
stop("Invalid value for data.row:\nMust be a valid rownames(data) or row-index value")
}
if (is.null(main))
main = rownames(data)[data.row]
if (scale == T) {
data = scale(data[, y.cols])
data = apply(data, 2, function(x) x/max(abs(x)))
}
data = as.data.frame(data)
n.y = length(y.cols)
min.rad = 360/n.y
polar.vals = (90 + seq(0, 360, length.out = n.y + 1)) * pi/180
#
if (add == F) {
plot(0, xlim = c(-2.2, 2.2), ylim = c(-2.2, 2.2), type = "n", axes = F,
xlab = "", ylab = "")
title(main)
lapply(polar.vals, function(x) lines(c(0, 2 * cos(x)), c(0, 2 * sin(x))))
lapply(1:n.y, function(x) text(2.15 * cos(polar.vals[x]), 2.15 * sin(polar.vals[x]),
y.cols[x], cex = 0.8))
lapply(seq(0.5, 2, 0.5), function(x) lines(x * cos(seq(0, 2 * pi, length.out = 100)),
x * sin(seq(0, 2 * pi, length.out = 100)), lwd = 0.5, lty = 2, col = "gray60"))
lines(cos(seq(0, 2 * pi, length.out = 100)), sin(seq(0, 2 * pi, length.out = 100)),
lwd = 1.2, col = "gray50")
}
r = 1 + data[data.row, y.cols]
xs = r * cos(polar.vals)
ys = r * sin(polar.vals)
xs = c(xs, xs[1])
ys = c(ys, ys[1])
lines(xs, ys, col = col, lwd = 2, lty = lty)
}
</code></pre>
<p>Using the <strong>mtcars</strong> data set:</p>
<pre><code class="r">webplot(mtcars)
</code></pre>
<p><img src="data:image/png;base64,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" alt="plot of chunk f"/> </p>
<p>Basically, we take a data frame, scale all numeric columns, and then plot how far above/below average (the thick black line) each of the values are for a particular row of data.</p>
<p>Here are the Arguments:</p>
<ul>
<li><strong>data</strong> - data.frame or matrix</li>
<li><strong>data.row</strong> - row of data to plot (if NULL uses row 1)</li>
<li><strong>y.cols</strong> - columns of interest (if NULL it selects all numeric columns)</li>
<li><strong>main</strong> - title of plot (if NULL then rowname of data)</li>
<li><strong>add</strong> - whether the plot should be added to an existing plot</li>
<li><strong>col</strong> - color of the data line</li>
<li><strong>lty</strong> - lty of the data line</li>
</ul>
<p>For example, we can change the data row that we plot, as well as the columns we want to include</p>
<pre><code class="r">webplot(mtcars, 2, y.cols = c("mpg", "cyl", "disp", "hp"))
</code></pre>
<p><img src="data:image/png;base64,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" alt="plot of chunk unnamed-chunk-2"/> </p>
<p>It turns out that this isn't the easiest way to compare results, it might be helpful to overlay plots</p>
<pre><code class="r">par(mfcol = c(1, 2))
webplot(mtcars, "Mazda RX4")
webplot(mtcars, "Mazda RX4 Wag")
</code></pre>
<p><img 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" alt="plot of chunk unnamed-chunk-3"/> </p>
<pre><code class="r">par(mfcol = c(1, 1))
</code></pre>
<pre><code class="r">par(mar = c(1, 1, 2, 1))
webplot(mtcars, "Mazda RX4", main = "Compare Cars")
webplot(mtcars, "Mazda RX4 Wag", add = T, col = "blue", lty = 2)
par(new = T)
par(mar = c(0, 0, 0, 0))
plot(0, type = "n", axes = F)
legend("bottomright", lty = c(1, 2), lwd = 2, col = c("red", "blue"), c("Mazda RX4",
"Mazda RX4 Wag"), bty = "n")
</code></pre>
<p><img 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<p>Which makes it easy to observe that the Mazda RX4 and Mazda RX4 Wagon are very similar, with the Wagon being a little heavier, and takes a little longer to travel a quarter mile</p>
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<span style="font-family: Arial, Helvetica, sans-serif;">In a </span><a href="http://statisticstoproveanything.blogspot.com/2010/09/charts-of-different-pch-values-in-r.html" style="font-family: Arial, Helvetica, sans-serif;" target="_blank">previous post</a><span style="font-family: Arial, Helvetica, sans-serif;"> I show how one can use custom pch values to represent different data types. I've long wanted to be able to take a custom image and use that to represent the data. </span><span style="font-family: Arial, Helvetica, sans-serif;">I recently discovered the </span><i style="font-family: Arial, Helvetica, sans-serif;">rasterImage</i><span style="font-family: Arial, Helvetica, sans-serif;"> function in R, which allows the user to take an image and plot it! There are various examples out there of using RasterImage (such as </span><a href="http://journal.r-project.org/archive/2011-1/RJournal_2011-1_Murrell.pdf" style="font-family: Arial, Helvetica, sans-serif;" target="_blank">RJournal_2011-1_Murrell.pdf</a><span style="font-family: Arial, Helvetica, sans-serif;">)</span><span style="font-family: Arial, Helvetica, sans-serif;">, but I didn't find anything that did exactly what I wanted it to do</span><br />
<br />
<span style="font-family: Arial, Helvetica, sans-serif;">the tricky part is that rasterImage requires you to define the 4 boundaries of the image. The goal is then to be able to define the boundaries by only specifying an x, y coordinate, and have code smart enough to display the image with the appropriate dimensions</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<br />
Here are the required packages<br />
<pre><code class="r">library(RCurl) #for reading file from a URL
</code></pre>
<pre><code>## Loading required package: bitops
</code></pre>
<pre><code class="r">library(png) #for reading in a .png, use library(jpeg) for a .jpg
</code></pre>
The function I wrote takes the image, the (x,y) coordinates of where you want to plot your image, and for now a <em>cex</em> and a <em>pos</em> argument. I intend on expanding the options, and hopefully will improve these functionalities over time.<br />
<br />
<pre><code class="r">image_points = function(image, x, y, cex = 1, pos = NULL) {
if (length(x) != length(y)) {
stop("length(x)!=length(y): check your data")
}
dim.x = dim(image)[2] #image width
dim.y = dim(image)[1] #image height
if (dim.x == dim.y) {
# obtian the ratio of width to height or height to width
ratio.x = ratio.y = 1
} else if (dim.x < dim.y) {
ratio.x = dim.x/dim.y
ratio.y = 1
} else {
ratio.x = 1
ratio.y = dim.y/dim.x
}
cex = cex/10 #how large the image should be, divided by 10 so that it matches more closely to plotting points
pin = par()$pin #pin provides the width and height of the _active graphic device_
pin.ratio = pin/max(pin) #take the ratio
usr = par()$usr #usr provides the lower.x, lower.y, upper.x, upper.y values of the plotable region
# combine the active device dimensions, the image dimensions, and the
# desired output size
image.size.y = (usr[4] - usr[3]) * pin.ratio[1] * cex
image.size.x = (usr[2] - usr[1]) * pin.ratio[2] * cex
for (i in 1:length(x)) {
# plot each point pos can be NULL (default) or 1, 2, 3, or 4, corresponding
# to centered (defualt), bottom, left, top, right, respectively.
if (is.null(pos)) {
# centered at (x,y), define the bottom/top and left/right boundaries of the
# image
x.pos = c(x[i] - (image.size.x * ratio.x)/2, x[i] + (image.size.x *
ratio.x)/2)
y.pos = c(y[i] - (image.size.y * ratio.y)/2, y[i] + (image.size.y *
ratio.y)/2)
rasterImage(image, x.pos[1], y.pos[1], x.pos[2], y.pos[2])
} else if (pos == 1) {
x.pos = c(x[i] - (image.size.x * ratio.x)/2, x[i] + (image.size.x *
ratio.x)/2)
y.pos = c(y[i] - (image.size.y * ratio.y), y[i])
} else if (pos == 2) {
x.pos = c(x[i] - (image.size.x * ratio.x), x[i])
y.pos = c(y[i] - (image.size.y * ratio.y)/2, y[i] + (image.size.y *
ratio.y)/2)
} else if (pos == 3) {
x.pos = c(x[i] - (image.size.x * ratio.x)/2, x[i] + (image.size.x *
ratio.x)/2)
y.pos = c(y[i], y[i] + (image.size.y * ratio.y))
} else if (pos == 4) {
x.pos = c(x[i], x[i] + (image.size.x * ratio.x))
y.pos = c(y[i] - (image.size.y * ratio.y)/2, y[i] + (image.size.y *
ratio.y)/2)
}
rasterImage(image, x.pos[1], y.pos[1], x.pos[2], y.pos[2]) #plot image
}
}
</code></pre>
I pulled an image from sweetclipart.com using <b>getURLContent()</b> and <b>readPNG()</b><br />
<br />
<pre><code class="r">URL = ("http://sweetclipart.com/multisite/sweetclipart/files/imagecache/middle/sports_car_2_red.png") #where the image is located
image = readPNG(getURLContent(URL)) #gets the content of the URL
</code></pre>
<strong>image</strong> is an array of dimensions <em>width</em> \( \times \) <em>height</em> \( \times \) <em>channels</em>. The first 3 channels represent the R, G, and B values (scaled 0 to 1) of each pixel, with the 4th channel representing the alpha value (scaled 0 to 1, 0 representing transparent)<br />
Only pngs have the alpha channel, so jpegs will have 3 channels. Not all pngs have the 4th channel, if they do have the 4th channel the background won't necessarily be transparent. More on alpha values in a bit<br />
<br />
<pre><code class="r">dim(image) #width, height, alpha
</code></pre>
<pre><code>## [1] 275 550 4
</code></pre>
<br />
Using the <strong>cars</strong> dataset we can plot the distance it took to stop by speed<br />
<br />
<pre><code class="r">data(cars)
plot(cars, type = "n", axes = F, xlab = "Speed", ylab = "Distance to Stop",
main = "Cars: Distance to Stop by Speed")
axis(1)
axis(2, las = 2)
x = cars$speed
y = cars$dist
image_points(image, x, y, 2)
</code></pre>
<img alt="Cars using Cars" src="data:image/png;base64,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" /> <br />
It turns out that the data is from the 1920s, so using this image might be more appropriate:<br />
<br />
<pre><code class="r">library(jpeg)
URL2 = "http://embed.polyvoreimg.com/cgi/img-thing/size/y/tid/4985430.jpg"
image2 = readJPEG(getURLContent(URL2))
plot(cars, type = "n", axes = F, xlab = "Speed", ylab = "Distance to Stop",
main = "Cars: Distance to Stop by Speed\n1920's car")
axis(1)
axis(2, las = 2)
image_points(image2, x, y, 2)
</code></pre>
<img alt="Cars using Cars" 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" /> <br />
Here we have a jpeg file that is a <em>width</em> \( \times \) <em>height</em> matrix with values 0 to 1 representing the black/white/gray scale. We can manipulate the data using <strong>rgb()</strong> and <strong>abind()</strong> to create an array with the appropriate R, G, B, and alpha values.<br />
First, on this color scale, values that are closer to 1 are going to be lighter gray to white, so we can assign an alpha value of 0 (transparent) to any values that are greater than 0.8.<br />
<br />
<pre><code class="r">alpha.val = matrix(1, nrow(image2), ncol(image2)) #want a matrix of 1s (not transparent) the same size as the image
alpha.val[image2 > 0.8] = 0 #for lighter gray and white values, set alpha to 0 (transparent)
</code></pre>
We then want to create a new array, and will set the first dimension to the original values. Because it is gray colors, R=G=B<br />
<br />
<pre><code class="r">library(abind)
image2.adj = array(image2, dim = c(nrow(image2), ncol(image2), 1))
image2.adj = abind(image2.adj, image2, image2, alpha.val)
</code></pre>
We can then plot it:<br />
<br />
<pre><code class="r">plot(cars, type = "n", axes = F, xlab = "Speed", ylab = "Distance to Stop",
main = "Cars: Distance to Stop by Speed\n1920's Car w/Transparency")
axis(1)
axis(2, las = 2)
image_points(image2.adj, x, y, 2)
</code></pre>
<img alt="Cars using Cars" src="data:image/png;base64,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" /> <br />
Notice that we have now essentially removed the border around the image, and even though the images overlap, we get a better sense of whwere the points lie.<br />
<h4>
A few final notes</h4>
<ul>
<li>If we want the cars to be reversed, we can simply…</li>
</ul>
<pre><code class="r">image2.adj.reversed = image2.adj[, ncol(image2.adj):1, ]
plot(cars, type = "n", axes = F, xlab = "Speed", ylab = "Distance to Stop",
main = "Cars: Distance to Stop by Speed\n1920's car w/Transparency, Reversed")
axis(1)
axis(2, las = 2)
image_points(image2.adj.reversed, x, y, 2)
</code></pre>
<img alt="Cars using Cars" src="data:image/png;base64,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" /> <br />
<ul>
<li>Using images with lower resolution will often yield better results, I don't know if there are better ways to display images at a lower resolution</li>
<li>There might be better ways to do what I've figured out here - perhaps there are some more <em>par</em> values that would help convert the resolution and control the cex value?</li>
</ul>
Anonymoushttp://www.blogger.com/profile/02697157095904133223noreply@blogger.com0tag:blogger.com,1999:blog-4272105618179300500.post-76310723776640323572013-05-19T23:29:00.002-07:002013-05-19T23:31:48.691-07:00Keep R Rockin' Me Baby<div class="tr_bq">
<span style="font-family: Arial, Helvetica, sans-serif;">I've been to Phoenix, AZ. I know I've been to Seattle, but
I'm not sure if I made it to Tacoma. I once rode the train from DC to NY, which
had at least one stop in Philadelphia. I've somehow never been to Atlanta, not
even for a layover; I've been to L.A., and I've seen Northern California.</span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">In the song "Rockin' Me" </span><span style="font-family: Arial, Helvetica, sans-serif;">Steve Miller travels to all these destinations. He does so, he first claims, to be with his “sweet
baby,” only a few verses later "just to hear [his] sweet baby say 'Keep on a
rockin' me baby.'" The thing I don’t really understand, however, is <i>why</i> he needs to visit these locations.<o:p></o:p></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">One thought, based on the first verse, is that he
is travelling to all of these cities looking real hard to find a job. Another theory
is he has found a job which requires his travel. Perhaps he’s just stalking this girl, but I kind of always thought he was just on a concert tour.<o:p></o:p></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">Regardless of the reason, I’ve found the list of
cities to be curious. We start out in Phoenix, a southwestern US city, and the
only city listed in which the state is named. He might name the state to ensure that we don't get it confused with one of <a href="http://en.wikipedia.org/wiki/List_of_places_named_for_the_phoenix">the other 6 cities/towns named Phoenix</a>, but I think that it’s probably because Arizona is a near-rhyme with the next city: Tacoma. From
the southwest to the northwest, we round off the four corners of the country
with Philadelphia and Atlanta, only to end up back on the west coast in L.A.
From there it’s just a short trip up the coast to Northern California (<a href="https://www.google.com/search?q=northern+california&rlz=1C1CHFX_enUS470US470&aq=0&oq=northern+cali&aqs=chrome.0.0j57j60l2j65l2.2105j0&sourceid=chrome&ie=UTF-8#rlz=1C1CHFX_enUS470US470&sclient=psy-ab&q=latitude+and+longitude+of+northern+california&oq=latitude+and+longnorthern+california&gs_l=serp.3.0.0i7i30.8586.12020.0.12896.19.17.1.0.0.2.130.1369.16j1.17.0...0.0...1c.1.14.psy-ab.spTuA0gQcB8&pbx=1&bav=on.2,or.r">38.2813° N, 120.9045° W</a>), where the Steve Miller Band happened to call home. I
really don’t know if I am just reading too much into the lyrics, but that is a <i>long </i>trip! How long? Well, I thought I’d
approximate it:</span></div>
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhm5wvZuirXjQPnpfgN5d7-FVNGO_3j8vPUOf4pwckVnjOrqaQDs2SAePZ6dbrBPTrBLiqMrl9VN6nQ3dlK1iPS66XxyOEtkoNvTALCB-0tFcNIY3PMnLxB8jE_LkLWq0SwFZhzXfTlST4/s1600/rockinmebaby.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhm5wvZuirXjQPnpfgN5d7-FVNGO_3j8vPUOf4pwckVnjOrqaQDs2SAePZ6dbrBPTrBLiqMrl9VN6nQ3dlK1iPS66XxyOEtkoNvTALCB-0tFcNIY3PMnLxB8jE_LkLWq0SwFZhzXfTlST4/s1600/rockinmebaby.gif" height="411" width="640" /></span></a></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><span id="goog_503674627"></span><span id="goog_503674628"></span></span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">So that’s really it - I wanted to know how far this alleged trip was, and if past the convenient rhymes and less convenient proximities, if there were any patterns that emerged from plotting out this odyssey.<o:p></o:p></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">The answer - no.</span></div>
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</div>
<br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<br />
<h4>
<span style="font-family: Arial, Helvetica, sans-serif;">R Code:</span></h4>
<br />
<blockquote>
library(maps)<br />
library(animation)<br />
cities = c("Phoenix, AZ","Tacoma","Philadelphia","Atlanta","L.A.","Northern California")<br />
lat = c(33.4492,47.2531,39.9522,33.7489,34.0522,38.2813)<br />
long = -c(112.0739,122.4431,75.1642,84.3881,118.2428,120.9045)<br />
distance = c(1093,2381,658,1938,336)<br />
<br />
m=map("state", interior = T)<br />
par(mar=c(0,0,0,0))<br />
par(mar=c(5,4,4,2)+.1)<br />
y.seq = x.seq=NULL<br />
slope = rep(NA,length(lat)-1)<br />
int = rep(NA,length(lat)-1)<br />
d=NULL<br />
for(i in 2:length(lat)-1) {<br />
slope[i] = (lat[i+1]-lat[i])/(long[i+1]-long[i])<br />
int[i] = lat[i]-slope[i]*long[i]<br />
<br />
l.out = sqrt((long[i]-long[i+1])^2 + (lat[i]-lat[i+1])^2)<br />
<br />
x.seq[[i]] = seq(long[i],long[i+1],length.out=l.out)<br />
y.seq[[i]] = int[i] + x.seq[[i]]*slope[i]<br />
<br />
a1 = lat[i]<br />
a2 = lat[i+1]<br />
b1 = long[i]<br />
b2 = long[i+1]<br />
d[[i]] = seq(0,distance[i],length=l.out)<br />
}<br />
x.seq[[5]] = c(x.seq[[5]],rep(x.seq[[5]][5],10))<br />
y.seq[[5]] = c(y.seq[[5]],rep(y.seq[[5]][5],10))<br />
d[[5]] = c(d[[5]],rep(d[[5]][5],10))<br />
for(x in 2:5) {<br />
d[[x]] = d[[x]]+d[[x-1]][length(d[[x-1]])]<br />
}<br />
<br />
saveGIF({<br />
for(i in 1:5) {<br />
for(j in 1:length(x.seq[[i]])) {<br />
plot(m,type="l",axes=F,col="steelblue",xlab="",ylab="",<br />
main="Rockin' Me")<br />
#map("state", boundary = FALSE, col="gray70", add = TRUE)<br />
<br />
points(long[0:i+1],lat[0:i+1],cex=.7,pch=16)<br />
text(long[0:i+1],lat[0:i+1],cities[0:i+1],pos=c(1,3,3,1,1,3)[0:i+1],cex=1.1,col="red")<br />
text(-98.5795,39.5285,paste(round(d[[i]][j]),"Miles"),cex=1.3,col="blue2")<br />
if(i>1) {<br />
for(q in 1:(i-1)) {<br />
lines(x.seq[[q]],y.seq[[q]])<br />
} <br />
}<br />
lines(x.seq[[i]][c(1,j)],y.seq[[i]][c(1,j)])<br />
} <br />
}<br />
}, movie.name = "rockinmebaby.gif", interval = 0.03, nmax = 1000,<br />
ani.width = 930, ani.height = 600)</blockquote>
<br />
<br />Anonymoushttp://www.blogger.com/profile/02697157095904133223noreply@blogger.com0tag:blogger.com,1999:blog-4272105618179300500.post-59875216035330985572011-01-09T20:12:00.000-08:002011-01-09T20:12:20.952-08:00Some useful R functionsIts been a while. In that time there have been several instances when I've been in need of some of the following functions and I had to go digging through my old homeworks to find specific instances when I used them; so I thought they'd be worth posting on here.<br />
<br />
First the <span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;">proc.time()</span> function is useful to see the runtime of a program. Here's an example that will give the run time in seconds:<br />
<br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;">time <- proc.time()</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"># - run some function - #</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;">proc.time()[3] - time[3]</span><br />
<br />
Some of the functions that I wrote for missing data have proven to be quite useful as well. First I always forget the <span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;">is.na()</span> function and often confuse <span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;">complete.cases</span> with <span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;">na.omit</span><br />
<br />
<br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;">### Ways to find what values are missing</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;">complete.cases(sed) #T/F if row has any missing</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;">na.omit(sed) #gives only rows with no missing values</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;">is.na(sed)==F #have to use is.na as a logical argument, not ==NA</span><br />
<br />
Here are some functions that I think are quite useful and I am surprised they aren't available in R, or if they are, I don't know what they are called<br />
<br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;">### Identify cols that are entirely NA</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;">NA.cols<-function(X) {</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> cols<-apply(X,2,function(x) sum(is.na(x)))==nrow(X)</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> names(cols)<-colnames(X)</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> na.cols<-which(cols==T)</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> if(length(na.cols)==0) na.cols<-'Each column has at least one non NA value'</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> return(na.cols)</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;">}</span><br />
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"><br />
</span></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;">### Identify rows that are entirely NA (opposite of</span></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;">### complete.cases)</span></div><span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;">NA.rows<-function(X) {</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> rows<-apply(X,1,function(x) sum(is.na(x)))==ncol(X)</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> names(rows)<-rownames(X)</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> na.rows<-which(rows==T)</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> if(length(na.rows)==0) na.rows<-'Each row has at least one non NA value'</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> return(na.rows)</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;">}</span><br />
<br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"><br />
</span><br />
<br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;">### Identify cols that have no have no NA values (I guess you</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;">### could also transpose the data and do na.omit)</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;">complete.cols<-function(X) {</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> cols<-apply(X,2,function(x) sum(is.na(x)))==0</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> names(cols)<-colnames(X)</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> complete.cols<-which(cols==T)</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> if(length(complete.cols)==0) complete.cols<-'There are no complete variables'</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> return(complete.cols)</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;">}</span><br />
<div><span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"><br />
</span></div><br />
<br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"><br />
</span><br />
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><span class="Apple-style-span" style="font-family: 'Times New Roman';">I also have my simple imputation function. For real imputation techniques I recommend the Amelia package (at least thats what I used for the multivariate class, and it seemed to have some nice features). I found using proc.time() that it takes like 22 seconds to run on my machine, mostly because the 'hot deck' imputation could probably be more efficient. The real lesson here is that when you write a function, you get to name it after yourself</span></span><span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"><br />
</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;">### A function that returns some simple imputation methods</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;">Alan.imputations<-function(X) {</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> require(fields)</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"><br />
</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> mean.x<-rep(NA,ncol(X))</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> median.x<-rep(NA,ncol(X))</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> min.x<-rep(NA,ncol(X))</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> max.x<-rep(NA,ncol(X))</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"><br />
</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> X.mean<-X</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> X.median<-X</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> X.min<-X</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> X.max<-X</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> X.zero<-X</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> X.sample<-X</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"><br />
</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> for(j in 1:ncol(X)) {</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> if(is.numeric(X[,j])==T) {</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> mean.x[j]<-mean(X[,j],na.rm=T)</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> median.x[j]<-median(X[,j],na.rm=T)</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> min.x[j]<-min(X[,j],na.rm=T)</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> max.x[j]<-max(X[,j],na.rm=T)</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> }</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> }</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> for(j in 1:ncol(X)) {</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> X.mean[is.na(X.mean[,j]),j]<-mean.x[j]</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> X.median[is.na(X.median[,j]),j]<-median.x[j]</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> X.min[is.na(X.min[,j]),j]<-min.x[j]</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> X.max[is.na(X.max[,j]),j]<-max.x[j]</span><br />
<br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> i.na<-is.na(X[,j])</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> if(sum(i.na)!=length(i.na))</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> X.sample[i.na,j]<-sample(na.omit(X[,j]),sum(i.na),replace=T)</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> }</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> X.zero[is.na(X.zero)]<-0</span><br />
<br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> cols<-apply(X,2,function(x) sum(is.na(x)))==nrow(X)</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> na.cols<-which(cols==T)</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> comp.X<-na.omit(X[,-na.cols])</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> numeric.cols<-rep(NA,ncol(comp.X))</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> for(i in 1:ncol(comp.X)) { </span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> numeric.cols[i] <- is.numeric(comp.X[,i])</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> }</span><br />
<br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> X.na<-X[,-na.cols];X.na<-X.na[,numeric.cols]</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> NA.index<-which(is.na(X.na)==T,arr.ind=T)</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> sX <- scale(X.na)</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"><br />
</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> X.na.center<-X.na - matrix(attr(sX,"scaled:center"),nrow(X.na),ncol(X.na),byrow=T)</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> X.na.scaled<-X.na.center/matrix(attr(sX,"scaled:scale"),nrow(X.na.center),ncol(X.na.center),byrow=T)</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> new.na.cols<-NA.cols(X.na.scaled)</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> X.na.scaled<-X.na.scaled[,-new.na.cols]</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> new.complete.cols<-complete.cols(X.na.scaled)</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"><br />
</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"><br />
</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> dist<-matrix(NA,nrow(X.na.scaled),nrow(X.na.scaled))</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> for(i in 1:nrow(X.na.scaled)) {</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> dist[i,]<-rdist(X.na.scaled[i,new.complete.cols],X.na.scaled[,new.complete.cols])</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> }</span><br />
<br />
<br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> for(i in 1:nrow(dist)) {</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> if(complete.cases(X.na.scaled)[i]==F) {</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> j<-2</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> min<-which(dist[i,]==dist[i,order(dist[i,])[j]])</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> while(sum(is.na(X.na.scaled[min,is.na(X.na.scaled[i,])]))!=0) {</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> min<-which(dist[i,]==dist[i,order(dist[i,])[j]])</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> j<-j+1</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> }</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> X.na.scaled[i,is.na(X.na.scaled[i,])]<- X.na.scaled[min,is.na(X.na.scaled[i,])]</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> } </span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> }</span><br />
<br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> X.hotdeck<-X.na.scaled*matrix(attr(sX,"scaled:scale")[-new.na.cols],nrow(X.na.scaled),ncol(X.na.scaled),byrow=T)+matrix(attr(sX,"scaled:center")[-new.na.cols],nrow(X.na.scaled),ncol(X.na.scaled),byrow=T)</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"><br />
</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> alan<-list(max=X.max, mean=X.mean, median=X.median, min=X.min, sample=X.sample, zero=X.zero, hotdeck=X.hotdeck)</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"> return(alan)</span><br />
<span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;">}</span><br />
<br />
<br />
(note that some of the spacing gets messed up, just in case something doesn't run right)Anonymoushttp://www.blogger.com/profile/02697157095904133223noreply@blogger.com2tag:blogger.com,1999:blog-4272105618179300500.post-2357311924847117572010-10-25T20:37:00.002-07:002010-10-25T21:08:39.362-07:00How to Compare Boozer and JeffersonI am a big fan of basketball, and my favorite team has always been the Utah Jazz. This past summer Carlos Boozer, the Jazz's starting Power Forward left the team to join the Chicago Bulls via a <a href="http://www.deseretnews.com/article/700046560/Utah-Jazz-Carlos-Boozer-sign-and-trade-agreement-reached-with-Bulls.html">sign-and-trade</a>. This allowed for Carlos Boozer to sign a larger contract, and gave the jazz a "trade exception." Basically a trade exception allows for a team to be involved in a trade with another team where the first team receives players with contracts worth more than what the first team sends away (see <a href="http://en.wikipedia.org/wiki/NBA_Salary_Cap#Other_exceptions">NBA Salary Cap: Other exceptions</a>). The Jazz then turned around, and with the help of their exception <a href="http://www.deseretnews.com/article/700047858/Utah-Jazz-Al-Jefferson-trade-a-done-deal.html">traded for</a> Al Jefferson in exchange for Kosta Koufos, 2 draft picks, and a bag of potato chips (well, pretty much). At the end of the day, its essentially like the Jazz exchanged Boozer for Jefferson.<br />
<div><br />
</div><div>On July 7th, just days before the Jefferson trade, the Deseret News reported <a href="http://www.deseretnews.com/article/700046383/Utah-Jazz-fans-have-mixed-reactions-about-Boozer.html">Utah Jazz fans have mixed reactions about Boozer</a>, where Boozer's tenure in Utah is summarized as being "polarizing". Boozer was an All-Star caliber player, but missed a third of his games in Utah, and many fans felt that last year he <a href="http://www.deseretnews.com/article/705314143/Boozer-and-Jazz-are-forced-to-be-back-together.html">didn't want to be back in Utah</a>. Either way, losing Boozer was going to impact the future of the Jazz.<br />
<br />
After the trade, however, the future of the Jazz seemed much brighter. If nothing else, Al Jefferson was <a href="http://www.deseretnews.com/article/700051432/Utah-Jazz-basketball-Al-Jefferson-talks-up-playing-in-Utah-in-interviews-with-national-media.html">excited</a> to be in Utah, and who wouldn't be after being on the Timberwolves? I'm excited for Al Jefferson, and my friends who are fans of the Utah Jazz on facebook seem to be as well. Bill Simmons is also excited for Jefferson, he writes in his <a href="http://sports.espn.go.com/espn/page2/story?page=simmonsnfl2010/101015&sportCat=nba">must-see list</a> column:<br />
<blockquote><span class="Apple-style-span" style="color: #333333; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 12px; line-height: 17px;">On a personal note, I loved Big Al on the Celtics, rooted for him in Minnesota, felt like a proud dad when his career was taking off in January '08, agonized for him when he blew out his knee that same month, then felt terrible last season as he struggled through one of the worst situations in recent memory. Seeing Jefferson get a chance to rejuvenate his career with a top-four point guard and a top-four coach -- on a good team, in a city that gives a crap -- is one of my five favorite things about this upcoming season. So there.</span></blockquote><br />
<div>Simmons isn't the only one who thinks Jefferson has a chance to emerge as a star in Utah's system. Sekou Smith shares his opinion in his blog entry <a href="http://hangtime.blogs.nba.com/2010/10/14/big-als-time-to-shine/">Big Als Time To Shine!</a><br />
<blockquote><div style="color: #333333; font-family: Arial, sans-serif; line-height: 16px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 0px; padding-right: 0px; padding-top: 5px;"><span class="Apple-style-span" style="font-size: small;">While debating the merits of <strong style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">Al Jefferson</strong> over <strong style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">Carlos Boozer</strong> as the low post catalyst for the Utah Jazz, someone informed me that Jefferson’s numbers on losing teams don’t compare the stats Boozer put up in a winning situation in Utah the last six years.</span></div><div style="color: #333333; font-family: Arial, sans-serif; line-height: 16px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 0px; padding-right: 0px; padding-top: 5px;"><span class="Apple-style-span" style="font-size: small;">I snapped. Seriously, I lost it.</span></div><div style="color: #333333; font-family: Arial, sans-serif; line-height: 16px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 0px; padding-right: 0px; padding-top: 5px;"><span class="Apple-style-span" style="font-size: small;">When told that solid numbers on a bad team mean nothing, I couldn’t hold my tongue. It’s the most ridiculous thing I’ve heard. Jefferson’s work during his final season in Boston and his three seasons in Minnesota all speak to the talent he has honed during his six NBA seasons.</span></div><div style="color: #333333; font-family: Arial, sans-serif; line-height: 16px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 0px; padding-right: 0px; padding-top: 5px;"><span class="Apple-style-span" style="font-size: small;">It’s not his fault he’s been on bad teams in rebuilding situations at every stop. But to assume that his numbers (Jefferson was a 20-10 man during his three seasons in Minnesota and has career averages of 15.3 points, 8.7 rebounds and 1.2 blocks) are meaningless on a bad team is not only an insult to my basketball sensibilities, it’s also downright foolish.</span></div></blockquote>I like what Simmons and Smith have to say about Jefferson. Simmons sees Jefferson's potential and intangibles and recognizes that he can excel in the new situation he has found himself in. Smith sees Jefferson's numbers as a representation of the type of player that he is, and argues that the Jazz will at least be as good as they were with Boozer. I think they both make excellent points.<br />
<br />
David Berri disagrees, at least with Smith's posting. He responds to Smith's blog post on the website OpposingViews.com with his article: <a href="http://www.opposingviews.com/i/not-even-close-carlos-boozer-vs-al-jefferson">Not Even Close: Carlos Boozer vs. Al Jefferson</a> where he uses the metric WP48 to refute Smith's opinion. Essentially, Barri uses this metric to show that Boozer contributes more to his team's success than Jefferson does.<br />
<br />
I had never heard of the metric "WP48" before so I took a look at the provided links. WP48 stands for "Wins Produced per 48 minutes" and is calculated through a series of adjusting for how teams play and other players play at particular positions. Details are provided <a href="http://www.wagesofwins.com/CalculatingWinsProduced.html">here</a>. After reviewing the metric I decided that I'm not a fan, and I'd like to make a few points.<br />
<br />
I find it indefensible that the defensive aspect of the metric is averaged over the entire team, for the entire game, even when the player isn't playing! That means that a player is penalized/rewarded not only for the other 4 players on the court with them, but for every player that comes off the bench. Furthermore, some teams get away with having sub par defensive play from guards by having defensive big men patrolling the paint, or some other combination of good/bad defenders on the court at the same time. Both Boozer and Jefferson are known as sub par defenders, but the Jazz certainly had a better defensive team as a whole than the Timberwolves. Jefferson is thus penalized more than Boozer for defensive play by the metric.<br />
<br />
Despite the numerous adjustments made throughout the computation of the metric, it still seems most appropriate in comparing players on the same team, and at best it compares players that play similar styles on similar teams.<br />
<br />
The Timberwolves ran an offense that was terrible for Jefferson, the triangle just didn't work for them. They also didn't have an all-star point guard to get him the ball in good places. Boozer may have had a higher scoring efficiency, but that isn't surprising since he also played for a team with a more efficient offense.<br />
<br />
Although the metric adjusts for minutes played by per 48 minutes played, it still doesn't account for the spacing on the floor. What I mean specifically is that Kevin Love was one of the best rebounders in the league last year, and played in a way that was not cohesive with Al Jefferson being on the floor at the same time. The minutes they played together hurt Jefferson.<br />
<br />
Also, I am not a fan of reducing data of this sort down to a single number. Don't get me wrong, I realize the importance of being able to reduce high dimensional data to dimensions that are interpretable, but a single value in this case is just too much. I don't see why you can't compare different aspects of their game together and decide that in one player is better in those certain aspects.<br />
<br />
<br />
I don't have a good answer as to whether Jefferson will be better for the Jazz than Boozer. I don't know if there are good metrics for determining how well a player will do in a new system. I'm reminded of a conversation I once had with my former roommate Eric. I told him about how I was going to model my predictions for March Madness and Eric said "I just watch a lot of basketball and pick the teams that I think are better." In this case I'm going to trust the guys that watch a lot of basketball.<br />
<br />
I do have a method for comparing players though. A few weeks ago I made some biplots to help prepare myself for fantasy basketball. The center of the plot is the league average in each category for PFs, and the stats are "per game." Each player projects down onto the categories at a right angle. Boozer can be found just above DREB and Al Jefferson is between DREB and OREB in a little more toward the center. You'll have to click on the image and zoom in to really read the names.<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJ6FgbUZYa1lfy45LKrJDm6GIg-UXFB_rcPxxekKbJ3XzSW383mqcfJKMSgVpFL8wxp3iaNl4kSo5vp9RXMwfvic0sF-OoQuzKf7Yzb-OEUNsnI5msmJhfGbyymg48qsfmnnoHL06cCyA/s1600/power_f.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJ6FgbUZYa1lfy45LKrJDm6GIg-UXFB_rcPxxekKbJ3XzSW383mqcfJKMSgVpFL8wxp3iaNl4kSo5vp9RXMwfvic0sF-OoQuzKf7Yzb-OEUNsnI5msmJhfGbyymg48qsfmnnoHL06cCyA/s640/power_f.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Biplot of Power Fowards 09-10 NBA Season</td></tr>
</tbody></table><br />
I love these plots, they summarize a lot of information. It can be seen that Boozer clearly had a better statistical year last year than Jefferson, but not by relative much. Boozer looks like he puts up all-star numbers, while Jefferson looks like he is a top ten power forward. And again, this data is all from last year and doesn't tell us how Jefferson will do <i>this</i> year.<br />
<br />
I hope the title of this blog posting didn't mislead you into thinking I had a good answer. I'll have think about how to better model how well players would perform in different systems.</div></div>Anonymoushttp://www.blogger.com/profile/02697157095904133223noreply@blogger.com0tag:blogger.com,1999:blog-4272105618179300500.post-91542239929093478172010-10-18T10:37:00.004-07:002010-10-18T10:51:34.426-07:00My Favorite Online R ReferencesI don't by any means claim to be a great and efficient R programmer, but it is certainly something that I aspire to be. The most important thing I've found is that I don't have to use a lot of brain power trying to remember every R command created. I just have to remember that there are R commands that have the ability to do things I want, and then it just takes a moment or two to look up what I want.<br />
<div><br />
</div><div>From time to time I think I'll post some of my favorite functions on here that I always seem to forget about that make life easier. For example the "which" function, which can often be replaced by using brackets in a clever manner, but can be invaluable in other instances. Another is the "match" function, which is great when you have, say, a sub list of rownames from a full list that you want to do something with. Another interesting function that was useful last week was the "jitter" function, which adds a specified amount of random error elements in a vector</div><div><br />
</div><div>Some of my favorite online references are listed below. When I want to know how to do something in R, before searching through google, I'll often check these out first:</div><div><br />
</div><div><span class="Apple-style-span" style="font-size: 13px;"><a href="http://www.statmethods.net/index.html">Quick R</a></span><br />
<span class="Apple-style-span" style="font-size: 13px;"><a href="http://www.statmethods.net/index.html"></a></span>A great site which has examples of using R for many different types of statistical analyses</div><br />
<div><br />
<a href="http://addictedtor.free.fr/graphiques/">R Graph Gallery</a></div><div><span class="Apple-style-span" style="font-family: Arial;">A great collection of graphs and plots</span></div><div><span class="Apple-style-span" style="font-family: Arial;"><br />
</span></div><div><span class="Apple-style-span" style="font-family: Arial; font-size: small;"><a href="http://rgraphics.limnology.wisc.edu/index.php">http://rgraphics.limnology.wisc.edu/index.php</a></span></div><div><span class="Apple-style-span" style="font-family: Arial;">Some basic plotting examples</span></div><div><br />
</div><div><span class="Apple-style-span" style="font-family: Arial;"><a href="http://onertipaday.blogspot.com/">One R Tip A Day</a></span></div><div><span class="Apple-style-span" style="font-family: Arial;">I haven't explored this site as much, but it has some nice things</span></div><div><span class="Apple-style-span" style="font-family: Arial;"><br />
</span></div><div><span class="Apple-style-span" style="font-family: Arial;"><br />
</span></div><div><span class="Apple-style-span" style="font-family: Arial;">When I find myself googling for specific examples it often results in searching through the </span><span class="Apple-style-span" style="font-family: Arial;"><a href="http://tolstoy.newcastle.edu.au/R/">R mailing lists archive</a>. More likely than not it'll take a few rewordings of my question before I find exactly what I want. And </span><span class="Apple-style-span" style="font-family: Arial;">I somehow have overlooked the obvious help files in R found by typing in ?function, a</span><span class="Apple-style-span" style="font-family: Arial;">s well as the great manuals found on the </span><span class="Apple-style-span" style="font-family: Arial;"><a href="http://cran.r-project.org/">The Comprehensive R Archive Network</a></span></div>Anonymoushttp://www.blogger.com/profile/02697157095904133223noreply@blogger.com5tag:blogger.com,1999:blog-4272105618179300500.post-66019646456054429492010-10-03T15:37:00.000-07:002010-10-03T15:37:53.158-07:00Chart of different lty values in RHere we can see the lty values available in R:<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgYHz8T9udPIrAcxUFO_SjyV1G6ZBWKeTHs35k2kcaUBz5AzZ1MlHvXZ6xavybBXhWvwo1jxGs3BNKyTv4rdImjT3wviCONq7UYsApptXmgVA5IBG-s4wcvAalAe9VI273botgMCsyq2Z0/s1600/lty.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgYHz8T9udPIrAcxUFO_SjyV1G6ZBWKeTHs35k2kcaUBz5AzZ1MlHvXZ6xavybBXhWvwo1jxGs3BNKyTv4rdImjT3wviCONq7UYsApptXmgVA5IBG-s4wcvAalAe9VI273botgMCsyq2Z0/s1600/lty.png" /></a></div><div class="separator" style="clear: both; text-align: left;">Only a few options, but using different colors and lwd sizes allows for many different options. Below is an example of how using different lty values helps distinguish between different types of data:</div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghhR-HzV8kkL73LHXc2j1o1YcTp-6CrhXDnAQhOeqJnb4Eyv_2_6TeLeVf-WfupWNWcGbQs79ClUyeDK-W4qqTR6zI84bxJWRS9YEyAYmvlO30wDFz7ClgUkyh10SigcnrYX5gePlE74A/s1600/highway.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghhR-HzV8kkL73LHXc2j1o1YcTp-6CrhXDnAQhOeqJnb4Eyv_2_6TeLeVf-WfupWNWcGbQs79ClUyeDK-W4qqTR6zI84bxJWRS9YEyAYmvlO30wDFz7ClgUkyh10SigcnrYX5gePlE74A/s1600/highway.png" /></a></div><div class="separator" style="clear: both; text-align: left;">And the code:</div><div class="separator" style="clear: both; text-align: left;"></div><div class="separator" style="clear: both; text-align: left;">plot(1, type="n", axes=F, xlab="", ylab="",xlim=c(0,10),ylim=c(0,20),</div><div class="separator" style="clear: both; text-align: left;">main="List of lty values in R",cex.main=2)</div><div class="separator" style="clear: both; text-align: left;">lines(c(0,10),c(17,17),lwd=2,lty=1)</div><div class="separator" style="clear: both; text-align: left;">text(2,16,'lty = 1 (default)',pos=4)</div><div class="separator" style="clear: both; text-align: left;">lines(c(0,10),c(14,14),lwd=2,lty=2)</div><div class="separator" style="clear: both; text-align: left;">text(2,13,"lty = 2 -or- lty = 'dashed'",pos=4)</div><div class="separator" style="clear: both; text-align: left;">lines(c(0,10),c(11,11),lwd=2,lty=3)</div><div class="separator" style="clear: both; text-align: left;">text(2,10,"lty = 3 -or- lty= 'dotted'",pos=4)</div><div class="separator" style="clear: both; text-align: left;">lines(c(0,10),c(8,8),lwd=2,lty=4)</div><div class="separator" style="clear: both; text-align: left;">text(2,7,"lty = 4",pos=4)</div><div class="separator" style="clear: both; text-align: left;">lines(c(0,12),c(5,5),lwd=2,lty=5)</div><div class="separator" style="clear: both; text-align: left;">text(2,4,"lty = 5",pos=4)</div><div class="separator" style="clear: both; text-align: left;">lines(c(0,10),c(2,2),lwd=2,lty=6)</div><div class="separator" style="clear: both; text-align: left;">text(2,1,"lty = 6",pos=4)</div><div class="separator" style="clear: both; text-align: left;"><br />
</div><div class="separator" style="clear: both; text-align: left;">plot(1,type='n',axes=T,xlab='',ylab='',xlim=c(0,10),ylim=c(1,10),main='Plot of Highway Data',cex.main=2)</div><div class="separator" style="clear: both; text-align: left;">abline(3,.75,lwd=2)</div><div class="separator" style="clear: both; text-align: left;">abline(1,.75,lwd=3,lty='dashed',col='yellow2')</div><div class="separator" style="clear: both; text-align: left;">abline(-1,.75,lwd=2)</div><div class="separator" style="clear: both; text-align: left;">lines(c(4,5),c(5,5.75),lwd=25,col='grey')</div><div class="separator" style="clear: both; text-align: left;">points(3.7,4.7,bg='red',pch=23,cex=2.5)</div><div class="separator" style="clear: both; text-align: left;">lines(c(3,3.5),c(2.1,2.475),lwd=20,col='blue')</div><div class="separator" style="clear: both; text-align: left;">points(3.2,2.25,cex=2,pch=19,col='skyblue4')</div><div class="separator" style="clear: both; text-align: left;">lines(c(8,8.3),c(8.2,8.45),lwd=20,col='green4')</div><div class="separator" style="clear: both; text-align: left;">points(8.19,8.35,cex=2,pch=23,bg='green3',col='green4')</div><br />
<div><div><br />
</div></div>Anonymoushttp://www.blogger.com/profile/02697157095904133223noreply@blogger.com0tag:blogger.com,1999:blog-4272105618179300500.post-17223673811984426382010-09-24T17:41:00.001-07:002010-09-24T17:41:22.933-07:00Charts of different pch values in RI always forget what each pch values is and I always end up going to this site to see the list: <a href="http://rgraphics.limnology.wisc.edu/pch.php">http://rgraphics.limnology.wisc.edu/pch.php</a>. But I don't like having to click on the thumbnail image to then see the large version. Here is my version:<br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgziEq_8n18tAc-rqz49xaSbRAIJB81ooITToneCXwIbJfBbbk3pQj4hUBY6D2IjTeavJ4MjzFrceiTAGhPX0MFyqLKFSgF1yjrWHGN4uYPUmF-MezInaBN9RTA0ISH8hMOCRFwAyKQ8o8/s1600/pch.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgziEq_8n18tAc-rqz49xaSbRAIJB81ooITToneCXwIbJfBbbk3pQj4hUBY6D2IjTeavJ4MjzFrceiTAGhPX0MFyqLKFSgF1yjrWHGN4uYPUmF-MezInaBN9RTA0ISH8hMOCRFwAyKQ8o8/s1600/pch.png" /></a></div>I don't understand why it has the value '0', and if there is a difference between 16 and 19 I have no idea what it is. and of course 20 could just be 19 with cex=.5<br />
<br />
Here are some other pch options, basically any character on the keyboard can be used:<br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMA0MjFTVJsksPuVD0rlVtVpzlg-3qD_YHOjzQS2Divl1ajY-6NWQ2xNyoAnE-pXnio5GkrtafyLXcaR1Xokb_jIF4yfgm8yW65C3bNwAc6xjbQKtwtjKaMtwqDZ3oS0_6Cp9CzNeDrik/s1600/other_pch.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMA0MjFTVJsksPuVD0rlVtVpzlg-3qD_YHOjzQS2Divl1ajY-6NWQ2xNyoAnE-pXnio5GkrtafyLXcaR1Xokb_jIF4yfgm8yW65C3bNwAc6xjbQKtwtjKaMtwqDZ3oS0_6Cp9CzNeDrik/s1600/other_pch.png" /></a></div>Of course some of these are better than others. For example, if you are plotting financial data, it might be best to consider something like this:<br />
<div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEieyNcHex4lxXqfGA8ZKHHA7gtaLNgoH9iKx60T9W9tn-f7rLZvDPOitFlJzw9B7f1ABhIpAofFuw-VdJOHA1C0HuaWGFM-B9FsY4rvXjpMiuRiPN4nmSUvm0ExmJD33-BhOwx4-u1MUYs/s1600/fin_pch.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEieyNcHex4lxXqfGA8ZKHHA7gtaLNgoH9iKx60T9W9tn-f7rLZvDPOitFlJzw9B7f1ABhIpAofFuw-VdJOHA1C0HuaWGFM-B9FsY4rvXjpMiuRiPN4nmSUvm0ExmJD33-BhOwx4-u1MUYs/s1600/fin_pch.png" /></a></div><br />
Or if you have confusing data this may be appropriate:<br />
<div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_ZHesobCjaunvB4MpJgaPzPdcTjCsukFCKd5AiNuA9SqaYcrfG8T_RoGh0km-_rbLKhb-GZwdUh_a4mPxebyQ306Fn9Vm11QsI3_slVmaZs8v9KOOk_AidUzaU67l2rYetNm3Qwf9tKk/s1600/conf_pch.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_ZHesobCjaunvB4MpJgaPzPdcTjCsukFCKd5AiNuA9SqaYcrfG8T_RoGh0km-_rbLKhb-GZwdUh_a4mPxebyQ306Fn9Vm11QsI3_slVmaZs8v9KOOk_AidUzaU67l2rYetNm3Qwf9tKk/s1600/conf_pch.png" /></a></div><br />
And of course the purpose of using different pch characters is to easily distinguish different type of data on the same plot. For example, here we see the ^ characters representing Teepees, and the ~ characters representing water:<br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMNPii5SIIKRH6kByd-_P4crAE-b3R8i7wjYkdkvzTLOEaOEc7cotIyFlzNd0NPt14Ra7GY-o4K6AOiVRIDibNLpAwQAHnCopRT28rIfiqPu3Ehe3vJdpIy0ysBgFiDs-kTXHCGhWdx2Y/s1600/river_pch.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMNPii5SIIKRH6kByd-_P4crAE-b3R8i7wjYkdkvzTLOEaOEc7cotIyFlzNd0NPt14Ra7GY-o4K6AOiVRIDibNLpAwQAHnCopRT28rIfiqPu3Ehe3vJdpIy0ysBgFiDs-kTXHCGhWdx2Y/s1600/river_pch.png" /></a></div><br />
<div class="separator" style="clear: both; text-align: center;"></div>To choose a particular pch for a plot, the code is either plot(x,y,pch=16) or plot(x,y,pch='~')<br />
<br />
Source Code for above plots:<br />
plot(c(.5,10),c(0,18),col='transparent',axes=F,<br />
<br />
xlab='',ylab='',main='List of pch values in R',cex.main=2)<br />
points(5,17,pch=0,cex=2)<br />
text(5,16,'0')<br />
points(c(1,3,5,7,9),c(rep(14,5)),pch=c(1:5),cex=2)<br />
text(c(1,3,5,7,9),c(rep(13,5)),c('1','2','3','4','5'))<br />
points(c(1,3,5,7,9),c(rep(11,5)),pch=c(6:10),cex=2)<br />
text(c(1,3,5,7,9),c(rep(10,5)),c('6','7','8','9','10'))<br />
points(c(1,3,5,7,9),c(rep(8,5)),pch=c(11:15),cex=2,bg='blue')<br />
text(c(1,3,5,7,9),c(rep(7,5)),c('11','12','13','14','15'))<br />
points(c(1,3,5,7,9),c(rep(5,5)),pch=c(16:20),cex=2)<br />
text(c(1,3,5,7,9),c(rep(4,5)),c('16','17','18','19','20'))<br />
points(c(1,3,5,7,9),c(rep(2,5)),pch=c(21:25),bg='lightblue',cex=2)<br />
text(c(1,3,5,7,9),c(rep(1,5)),c('21','22','23','24','25'))<br />
<br />
plot(c(.5,10),c(0,10),col='transparent',axes=F,<br />
xlab='',ylab='',main='Some other pch values in R',cex.main=2)<br />
points(c(1,3,5,7,9),c(rep(9,5)),pch=c('A','a','0','O','o'),cex=2)<br />
points(c(1,3,5,7,9),c(rep(7,5)),pch=c('*','.','|','+'),cex=2)<br />
points(c(1,3,5,7,9),c(rep(5,5)),pch=c('^','_','-','/','#'),cex=2)<br />
points(c(1,3,5,7,9),c(rep(3,5)),pch=c('!','@','$','%','&'),cex=2)<br />
points(c(1,3,5,7,9),c(rep(1,5)),pch=c('(',')','<','>','~'),cex=2)<br />
mtext("Line 2", side=1, line=2, adj=0.0, cex=1, col="blue", outer=TRUE)<br />
<br />
x<-seq(1,10,by=0.3333)y<-10+.25*x+rnorm(length(x),0,.5)<br />
plot(x,y,pch='$',axes=F,main='Plot of Financial Data',cex.main=2,cex.lab=1.5)<br />
box()<br />
<br />
x<-seq(1,10,by=0.3333)y<-10+.25*x+rnorm(length(x),0,.5)<br />
plot(x,y,pch='?',axes=F,main='Plot of Confusing Data',cex.main=2,cex.lab=1.5)<br />
box()<br />
<br />
x<-seq(2,7,by=.02)<br />
y<-x+.25*x^3+rnorm(length(x),0,10)<br />
x2<-seq(3,5,by=0.06)<br />
y2<-22+10*x2+rnorm(length(x2),0,6)<br />
plot(x,y,pch='~',main='Plot of Village by a River',col='blue',cex=2,cex.main=2,cex.lab=1.5)<br />
points(x2,y2,pch='^',col='red',cex=2)Anonymoushttp://www.blogger.com/profile/02697157095904133223noreply@blogger.com5