Suppose that you fit the model
E(y) = β0 + β1x1 + β2x2 + β3x3
to 15 data points and found F equal to 57.44.
1. Do the data provide sufficient evidence to indicate that the model contributes information for the prediction of y? Test using a 5% level of significance (F0.05 = 3.59).
2. The computer output for the multiple regression analysis provides this information: b0 = 1.04, b1 = 1.29, SE(b1) = 0.42, b2 = 2.72, b3 = 0.41, SE(b2) = 0.65, SE(b3) = 0.17. Which, if any, of the independent variables x1, x2, x3 contribute information for the prediction of y (use α = 0.05 and t0.025 = 2.201)?
3. What is the practical interpretation of the parameter β1?