\fCorrelations of Height and Weight Weight Lengths Height Width 0.008- Corr: 0.932/ Corr: 0.804mm Corr: 0.91 1mm 0.004- Pike: 0.979mm Pike: 0.9:38mm Pike: 0.920mm 0.002- Roach: 0.918+ Roach: 0 892" Roach: 0:924" Weight (x). 000 Length 3 (y) Corr. 0.739 Corr: 0.912. 50 Pike 0.953+ Pike: 0.94 1 mm Length 3 (x); Height (y) Roach: 0 957 Roach: 0.9647. Density plot of Corr. 0.915+ height, by Pike: 0 987 species Roach: 0.951" 7- 500 1000 1500 20 30 40 50 10 Figure 2. Pairs plot showing scatterplots, density plots and correlations for all pairwise combinations of Weight, Length3, Height, and Width. Pink indicates the species Pike and light blue indicate Roach.\fProblem 2 [ll] points}: Five measurements; were taken on two species of sh from a single lake {n = 1? Pike and n : 2D Roach]. For this problem. sh weight is the response {y} and cross length. height and diagonal width are possible predictors of sh weight. This problem does not require any coding; rather. we are providing summary graphs. summary tables. and int output in the supplementary handout. a} b} a} Look at the density plot in the last row of Figure 2 and the histograms in Figure 6 of the supplementary handout [pages 3 and T] and describe the distribution for all the observed sample widths. Also compare the sample distributions for widths individually for Pike and Roach. You may also use the "iinumber summaries on page 3 if you nd that helpful. Use no more than four sentences. (LS points) Look at Figure 2 {page 3] ofthe supplementary handout and interpret the joint relationship for Weight on Width for all the data. Also comment on thejoint relationships when considering species. [Hint: make clear. specic observations regarding the relationships]. Use no more than three sentences. [1.5 points] Using Figure 2 {page 3]. what is the overall sample correlation between Height and Width. 1What are the correlations for Height and 1|Ip'ti'idth by species'iI How do correlations by species compare with the overall correlation? Use no more than two sentences. [1.5 points} Using the single variable lm output on page 9. write out the regression equation for Weight on He i ght. In one sentence. interpret the estimated slope parameter for this regression in the context of the problem. {1.5 point] Report and in one sentence interpret the coefficient of determination for the regression of Weight on Length3 in the context of the problem. [1.5 point} Look at the plots in the middle row of Figure 3 on page 1 1. These are residual diagnostic plots for the single variable regression of sh Weight on sh He ight. Consider three ofthe main assumptions for inference for linear regression {methods for inference will be covered in Lesson 8}: linearity. constant variance. and normality ofresiduals. Do any ofthe three assumptions appear to be violated for this regression? Explain in no more than three sentences. one for each assumption. {L5 points) On page 12 ofthe supplementary handout. we provide regression output for Weight on Width. and Weight: on Width with the additional categorical variable Species. Using the scatterplots with regression lines in Figure 7". page If]. for Weight on Width. which model (single regression all species or different slopes by species} do you think is best for predicting sh weight from sh width? Explain. limiting your answer to at most two sentences. [I point}