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.
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.
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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