Consider the following four datasets. Each one is of size n = 11. Each one contains the variables (x, y), for i = 1,2,3,4 where y; is the response and x; is the regressor (this dataset is also found in the Excel file provided in the tab labeled "Anscombe"). ## x1 x2 x3 x4 yl # # 1 10 10 10 8 8.04 %22%23 28 8 8 8 6.95 y2 y3 y4 9.14 7.46 6.58 8.14 6.77 5.76 ## 3 13 13 13 8 7.58 8.74 12.74 7.71 # # 4 9 9 9 8 8.81 8.77 7.11 8.84 #2 #3 5 11 11 11 8 8.33 9.26 7.81 8.47 ## 6 14 ## 7 6 14 14 8 9.96 8.10 8.84 7.04 8 7.24 6.13 6.08 5.25 ## 8 4 4 4 19 4.26 3.10 5.39 12.50 # # 9 12 12 12 8 10.84 9.13 8.15 5.56 # # 10 7 7 7 8 4.82 7.26 6.42 7.91 # # 11 5 5 5 8 5.68 4.74 5.73 6.89 a) Compute the R with two digits of precision in each of the four cases. What do you find? b) Recall that the standard assumptions for the simple regression analysis are the fol- lowing: i. The relationship between the response y and the regressor is linear, at least approximately. The error term has constant variance. ii. The error term has zero mean. iii. iv. v. The errors are uncorrelated. The errors are normally distributed. c) For each of the four datasets, discuss each of the 5 assumptions above - thus you will analyze these 4 x 5 = 20 cases. In each case, use a residual analysis to assess which assumptions are reasonable and which are not. d) Can you propose a transformation in the case of the second dataset that will make all assumptions likely to be fulfilled? If yes, propose such a transformation and conduct the regression analysis of the transformed data.