ProblemSet_2_08B solutions

ProblemSet_2_08B solutions - ESM problem set 2 solutions...

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ESM problem set 2 solutions Here are the answers to questions 1 and 2 for each of the datasets in turn. Chlorophyll: 1) Here is the sample covariance matrix: Chlorophyll-a Phosphoru s Nitrogen Chlorophyll-a 2401.908 Phosphorus 6061.834 20045.42 Nitrogen -133.992 -514.378 31.1584 Here is the sample correlation matrix: Chlorophyll-a Phosphoru s Nitrogen Chlorophyll-a 1 Phosphorus 0.873611 1 Nitrogen -0.48979 -0.65086 1 2) Here are the scatterplots between the three variables: 0 100 200 300 400 500 600 700 0 50 100 150 200 Chlorophyll-a Phosphorus
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0 5 10 15 20 25 30 0 50 100 150 200 Chlorophyll-a Nitrogen 0 100 200 300 400 500 600 700 0 5 10 15 20 25 30 Nitrogen Phosphorus The relationship between phosphorus and Nitrogen appears to be somewhat nonlinear, so that the correlation coefficient doesn’t fully describe the association.
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Norwegian Lakes: 1) Here is the sample covariance matrix: pH.1976 pH.1981 Lat Long SO4.1981 NO3.1981 pH.1976 0.386658 pH.1981 0.33053 0.325363 Lat 0.372857 0.349492 1.284603 Long 0.188432 -0.01032 -0.08238 4.194898 SO4.1981 -0.42491 -0.37409 -0.87921 2.672347 4.150862 NO3.1981 -26.7932 -23.839 -48.9841 38.22449 112.0074 7347.392 Here is the sample correlation matrix: pH.1976 pH.1981 Lat Long SO4.1981 NO3.1981 pH.1976 1 pH.1981 0.931886 1 Lat 0.529047 0.540591 1 Long 0.147955 -0.00883 -0.03549 1 SO4.1981 -0.3354 -0.3219 -0.38075 0.640417 1 NO3.1981 -0.50268 -0.48757 -0.5042 0.217728 0.641373 1 Note that the correlation between latitude and longitude is not particularly meaningful; it is not something that we would normally report. 2) Here are the scatterplots between the variables (made with Graphs → Scatterplot matrix in RCmdr):
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There appears to be relatively strong nonlinearity between NO3 and each of latitude and the two pH variables. SO4 may also be nonlinear with those variables, although not as strongly.
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1) Here is the sample covariance matrix: Area Natives Aliens GDP M_imports Duties Agr Pasture Pop_dens Prop_exotic Area 7.13E+12 Natives 7.4E+09 24201173 Aliens 1.08E+09 1682313 312290.4 GDP 5.55E+09 2631252 1751989 34437223 M_imports -1.8E+07 -40500.5 -4653.9 -19249.4 419.5972 Duties -9157789 -8824.53 -3089.51 -42594.2 49.67571 72.17301 Agr 3530269 32637.62 4216.587 -40426.2 -11.164 29.04498 608.7707 Pasture -1763493 8478.005 2167.84 -16419.7 -70.758 13.6875 222.6632 378.1649 Pop_dens -1.3E+08 -282852 -19358.1 342055.6 1254.276 240.5811 -659.654 -38.4914 58554.48 Prop_exotic -5662.25 -233.035 16.28424 539.3947 0.313187 -0.58379 -0.99469 0.070466 21.80066 0.020444 Here is the sample correlation matrix: Area Natives Aliens GDP M_imports Duties Agr Pasture Pop_dens Prop_exoti c Area 1 Natives 0.563493 1 Aliens 0.726742 0.611941 1 GDP 0.354182 0.091144 0.534242 1 M_imports -0.32159 -0.39904 -0.40067 -0.15741 1 Duties -0.34248 -0.18757 -0.5556 -0.84253 0.291105 1 Agr 0.053595 0.268889 0.305812 -0.2792 -0.02166 0.130449 1 Pasture -0.03278 0.086706 0.193839 -0.15263 -0.17948 0.083112 0.479243 1 Pop_dens -0.1968 -0.23761 -0.14315 0.240881 0.248227 0.373147 -0.11049 -0.01916 1 Prop_exotic
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This note was uploaded on 08/06/2008 for the course ESM 206 taught by Professor Kendall,berkley during the Spring '08 term at UCSB.

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ProblemSet_2_08B solutions - ESM problem set 2 solutions...

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