2. For question 2, import the data from https://raw. githubusercontent. com/hgweon2/data/main/hw3-data. txt The imported dataset contains 200 observations with 3 variables: y, x1 and x2. (a) Plot a scatterplot matrix and briefly discuss the relationships between the variables. (b) Obtain the fitted model: Y = Bo+ Air + 8202. Check the model assumptions using appropriate graphical and testings approaches. (c) Was there any influential point? Use Cook's distance with threshold = 4. Report the indices of the influential points. (d) Among the influential points, how many of them are also considered outliers (whose absolute standardized residuals are greater than 2)? (e) Suppose that the influential points identified in (c) were simple measurement errors. Remove the influential points from the data and repeat (b) using the updated data set. Was the removal of the influential points helpful for correcting the model assumptions? (f) Use the Box-Cox method to determine the best transformation on the response variable y (use all 200 observations). Repeat (b) using the transformed y. (For A, use a reasonable value near the optimal value). Was this transformation helpful for correcting the model assumptions? (g) This time, obtain the polynomial model: Y = Bo + Pix, + 82x2 + 83xi + Bax]. Is this polynomial model preferable to the resulting models in (b) and (f)? Justify your answer. (h) Add the cubic terms to the model. That is, obtain Y = At je, + Aziz + Bar; + Bar? + Asxi + Asx] Would this cubic model be preferred to the quadratic one in (g)? Justify your