1. Some Analysis of Some Perch Catch Data 56 perch were caught in a freshwater lake in Finland Their weights, lengths, heights and widths were recorded It may be anticipated that thefish's weights depend on their lengths, heights and widths whose product is a proxy for volume

2. Some questions/goals: summary outliers prediction interpretation of coefficients linear gaussian errors preparation for a comparative study presentation of results...

3. Some of the data. Weight(g) Length(cm) Height(cm) Width(cm) 5.9 8.4 2.11 1.41 32.0 13.7 3.53 2.00 40.0 15.0 3.82 2.43 51.5 16.2 4.59 2.63 70.0 17.4 4.59 2.94 100.0 18.0 5.22 3.32 78.0 18.7 5.20 3.12 summary(weight) Min. 1st Qu. Median Mean 3rd Qu. Max. 5.9 120.0 207.5 382.2 692.5 1100.0

4. stem() The decimal point is 2 digit(s) to the right of the | 0 | 134578899011222333345555789 2 | 0235567002 4 | 16 6 | 59900 8 | 224500 10 | 000200 The decimal point is 2 digit(s) to the right of the | 0 | 134578899 1 | 011222333345555789 2 | 0235567 3 | 002 4 | 5 | 16 6 | 599 7 | 00 8 | 2245 9 | 00 10 | 0002 11 | 00

5. ecdf()

6. qqnorm()

7. density()

8. boxplot()

10. library(lattice) splom

11. plot()

12. qqnorm()

13. summary(junk2) Call: lm(formula = logweight ~ loglength + logheight + logwidth) Residuals: Min 1Q Median 3Q Max -0.075575 -0.022514 -0.001842 0.022046 0.091880 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -1.0060 0.1690 -5.953 2.28e-07 *** loglength 1.6197 0.2265 7.151 2.84e-09 *** logheight 0.8226 0.2167 3.796 0.000386 *** logwidth 0.5622 0.1803 3.119 0.002958 ** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.03767 on 52 degrees of freedom Multiple R-squared: 0.994, Adjusted R-squared: 0.9937 F-statistic: 2890 on 3 and 52 DF, p-value: < 2.2e-16

14. qqnorm()

15. anova(junk2) Analysis of Variance Table Response: logweight Df Sum Sq Mean Sq F value Pr(>F) loglength 1 12.2353 12.2353 8623.0612 < 2.2e-16 *** logheight 1 0.0534 0.0534 37.6351 1.179e-07 *** logwidth 1 0.0138 0.0138 9.7278 0.002958 ** Residuals 52 0.0738 0.0014 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

16. logw = -1.0060 + 1.6197 logl +.8226 logh +.5622 logw (.1690) (.2265) (.2167) (.1803)

17. h i library(MASS) lm.influence()$hat

18. E i * = E i /[S (-i)  (1-h i )] qqline(studres())

19. E i *  [h i /(1-h i )] dffits

20. D i cooks.distance

22. library(car) av.plots()

23. junk3<-cbind(length-mean(length),width-mean(width),height- mean(height)) cor(junk3) [,1] [,2] [,3] [1,] 1.0000000 0.9746171 0.9855836 [2,] 0.9746171 1.0000000 0.9829435 [3,] 0.9855836 0.9829435 1.0000000

24. Is X'X near singular? Would make interpretation of coefficients difficult junk3<-cbind(length-mean(length),width-mean(width),height- mean(height)) junk4<-svd(junk3) junk4$d [1] 71.313882 3.927869 2.050682

25. Conclusions. Can replace weight by product of lengths Traditional linear model results not strongly invalidated Began with EDA, to look for unusual "things", then moved onto linear model...