Solution 8 12/4/2018 F P1 P2 RESI1 SRES1 TRES1 HI1 FITS1

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Solution 8 12/4/2018 F P1 P2 RESI1 SRES1 TRES1 HI1 FITS1 68 78 73 -4.64839 -1.24647 -1.26609 0.109800 72.6484 75 74 76 2.28885 0.61442 0.60407 0.111725 72.7111 85 82 79 6.36605 1.67143 1.76150 0.071444 78.6340 94 90 96 0.03474 0.00941 0.00916 0.128042 93.9653 86 87 90 -2.46803 -0.64693 -0.63672 0.068384 88.4680 90 90 92 -1.27712 -0.33888 -0.33084 0.090883 91.2771 86 83 95 -3.87486 -1.17900 -1.19199 0.308602 89.8749 68 72 69 0.96978 0.26369 0.25713 0.134232 67.0302 55 68 67 -8.73280 -2.47107 -2.91964 0.200563 63.7328 69 69 70 2.76276 0.77703 0.76862 0.190801 66.2372 91 91 89 1.25065 0.34009 0.33203 0.134383 89.7493 75 79 75 0.51920 0.13757 0.13396 0.088219 74.4808 81 89 84 -4.41249 -1.22480 -1.24218 0.169224 85.4125 91 93 97 -5.10231 -1.39159 -1.42926 0.139485 96.1023 80 87 77 0.26843 0.08266 0.08047 0.324901 79.7316 94 91 96 -0.45360 -0.12255 -0.11933 0.123109 94.4536 94 86 94 3.33216 0.91583 0.91175 0.152636 90.6678 97 91 92 5.23455 1.39977 1.43863 0.104862 91.7655 79 81 82 -1.16172 -0.30114 -0.29381 0.047421 80.1617 84 80 83 3.65458 0.95617 0.95390 0.064906 80.3454 65 70 66 0.96256 0.26818 0.26152 0.175399 64.0374 83 79 81 4.48699 1.17150 1.18381 0.060981 78.5130 12/4/2018

(b) The matrix plot shows F and P1, F and P2 have strong linearity relationship. Moreover, there is a collinearity between P1 and P2. 12/4/2018

(c) The matrix plot of the standardized residuals shows that the standardized residuals are linearly uncorrelated with P1 and P2. This is because the linearity effects of P1 and P2 have been removed. The collinearity relationship between P1 and P2 is still there since nothing has been changed between them. 12/4/2018

(d) The residual plots are as above (d) The residual plots are as above. Except one outlier, the normality assumption seems ok, linearity assumption seems ok, homogeneity may be slightly violated, independence assumption may be ok. 12/4/2018

(e) Except one outlier, the SRES1 and TRES1 are almost on the diagonal line, i.e. they are almost equal. 12/4/2018

(f) F is strongly linearly related with FITS1 (f) F is strongly linearly related with FITS1. The correlation between F and FITS1 is the multiple correlation coefficient, i.e., the squared root of R-square. 12/4/2018

(g) The index plot of the leverages shows that there are two high leverage points, whose leverages are more than 2(p+1)/n=6/22=.27. 12/4/2018