2. Consider the linear regression model y = Bo+ 1x1 + B2x2 + e. Suppose that...

  

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2. Consider the linear regression model y = Bo+ 1x1 + B2x2 + e. Suppose that the second and third columns of the design matrix X have mean zero and length one, that is r = 1 and the same for 22, and the sample correlations between these two columns is p. (a). Compute the X'X matrix and show that (b) Show that n 0 0 X'X = 0 1 0 1 1/n 0 0 (X'X)-1= 0 C -cp 0 - C 1 where c = (c) Compute and express Var (B1-B2) in terms of p, 02. (d) Determine the range of value(s) of p that will make the variance of the least squares estimators of B1 and B2 larger than 50. (e) Discuss the possible connection between the result in (d) and multicolinearity (variance inflation factor). 2. Consider the linear regression model y = Bo+ 1x1 + B2x2 + e. Suppose that the second and third columns of the design matrix X have mean zero and length one, that is r = 1 and the same for 22, and the sample correlations between these two columns is p. (a). Compute the X'X matrix and show that (b) Show that n 0 0 X'X = 0 1 0 1 1/n 0 0 (X'X)-1= 0 C -cp 0 - C 1 where c = (c) Compute and express Var (B1-B2) in terms of p, 02. (d) Determine the range of value(s) of p that will make the variance of the least squares estimators of B1 and B2 larger than 50. (e) Discuss the possible connection between the result in (d) and multicolinearity (variance inflation factor).