4. (From Weisberg. 2005.) We are interested in the linear model Y = 0, + 0 x, +0,x, +e. (a) Suppose we fit the model above to data for which x, = 2.2x, with no error (that is, all residuals-0). For example, X, could be a weight in pounds, and X, the weight of the same object in kg. Describe the appearance of the added-variable plot for x, after x, had been added to the model above. Explain why. Assume that Y has a correlation with the predictors that is neither 0 nor 1. Hint: Think about what goes on the x-axis and the y-axis of the added variable plot. You should notice something interesting about one of those residual vectors. (b) Again referring to the model above, this time suppose that Y and X, are perfectly correlated, so Y = 3X , without any error. Describe the appearance of the added-variable plot for x, after x, had been added to the model. Explain. Assume this time that the correlation between the predictors is between 0 and 1