Question: (From Weisberg, 2005.) We are interested in the linear model Y = ?0 + ?1x1 + ?2x2 + e. (a) Suppose we fit the model

(From Weisberg, 2005.) We are interested in the linear model Y = ?0 + ?1x1 + ?2x2 + e.

(a) Suppose we fit the model above to data for which x1 = 2.2x2 with no error (that is, all residuals=0). For example, X1 could be a weight in pounds, and X2 the weight of the same object in kg. Describe the appearance of the added-variable plot for x2 after x1 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 X1 are perfectly correlated, so Y = 3X1, without any error. Describe the appearance of the added-variable plot for x2 after x1 had been added to the model. Explain. Assume this time that the correlation between the predictors is between 0 and 1.

(From Weisberg, 2005.) We are interested in the linear model Y =

{From Weisberg, 24305.} We are interested in the linear model Y = g +1x1 +13sz + e. {all (bl Suppose we fit the model above to data For which x1 = 2.2x: with no error [that is, all residuals=}. For example. X1 could be a weight in pounds, and X2 the weight of the same object in kg. Describe the appearance of the addedvariable plot for x: after x1 had been added to the model above. Explain why. Assume that Y has a correlation with the predictors that is neither Cl nor 1. Hint: Think. about what goes on the xaxis and the yaxis of the added variable plot. You should notice something interesting about one of those residual 1rectors. Again referring to the model above, this time suppose that Y and X1 are perfectlyr correlated. so Y = 3.3.], without any error. Describe the appearance of the addedvariable plot for .372 after x1 had been added to the model. Explain. Assume this time that the correlation between the predictors is between {i and 1

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