The constant term is not always needed in the regression equation. For example, many physical principles involve proportions, where no con- stant term is needed. In general, if the dependent variable should be 0 when the independent vari- ables are 0, then the constant term is not needed. Then it is preferable to omit Bo and use the model Y = B, x1 + B2.X2 + ... + Bekk + E. Here focus on the special case k = 1. a. Differentiate the appropriate sum of squares to derive the one normal equation for estimat- ing Bı.
b. Express your normal equation in matrix terms, X'XB = X'y, where X consists of one column with the values of the predictor vari- able.
c. Apply part (b) to the data of Example 12.32, using hp for y and just engine size in X.
d. Explain why deletion of the constant term might be appropriate for the data set in part (c).
e. By fitting a regression model with a constant term added to the model of part (c), test the hypothesis that the constant is not needed.