The forecaster in Exercise 15.2 augments her AR(4) model for \(I P\) growth to include four lagged values of \(\Delta R_{t}\), where \(R_{t}\) is the interest rate on three-month U.S. Treasury bills (measured in percentage points at an annual rate).

a. The \(F\)-statistic on the four lags of \(\Delta R_{t}\) is 3.91. Do interest rates help predict IP growth? Explain.

b. The researcher also regresses \(\Delta R_{t}\) on a constant, four lags of \(\Delta R_{t}\), and four lags of \(I P\) growth. The resulting \(F\)-statistic on the four lags of \(I P\) growth is 1.48. Does \(I P\) growth help to predict interest rates? Explain.