4. The dataset "anscombe.txt" posted contains well-known data sets made up by Anscombe (1973). It illustrates that there are natures of data that cannot be captured by summary statistics, or by the fitted regression models, while graphs often reveal untold stories. The dataset contains 4 covariate response pairs, for variables (2(1), (1), ((2), Y (2)), [2(3),Y(3)), and z(4),(}. The variables (1) = x[2) = r(3), and their observations are given by the column "le3" in the dataset. The variable c(4) is given by the column \"34". The responses Y0, ...,Y () are given by the columns "yl", ..., "y4" in the dataset. (a) Draw a scatter plot for each covariate response pair, and put the 4 scatter plots in the same plot. Find the mean and standard deviation for each variable in the dataset. Compare the means across the covariates (x(1) and c{4), and across the responses (Y(1},...,Y(4)). Also compare the standard deviations. (b) Use Im() in R to fit a simple linear regression model to each covariate response pair and add the fitted line to the corresponding scatter plot. Specify your models. (c) Compare the 4 fitted models in terms of the estimates of the regression coefficients, and the RP. Does R9 tell you everything about the overall fit of the model? Is each model suit- able for the corresponding data? Discuss based on the graphical nature of the data {notice that the point far away from the majority for (c(4),y[)) is an influential point). (d) For the pair (x3),(3)), there is an outlying observation. Remove the outlier, and find the estimates for the regression coefficients; also find R2 by computing the ANOVA table. Use the formulas in Chapter 2