94. The constant term is not always needed in the regression equation. In general, if the dependent variable should be 0 when the independent variables are 0, then the constant term is not needed. Then it may be preferable to omit b0 and use the model y  b1x1 

b2x2  . . .  bkxk 

e. Here we focus on the special case k1.

a. Differentiate the appropriate sum of squares to derive the one normal equation for estimating b1.

b. Express your normal equation in matrix terms, XXB  Xy, where X consists of one column with the values of the predictor variable.

c. Apply the result from part

(b) to the data of Example 12.32, using hp for y and liters for X.

d. Explain why deletion of the constant term might be appropriate for the data set in part (c).

e. By tting a regression model with a constant term added to the model of part (c), test the hypothesis that the constant is not needed.