Testing Hypotheses About Regression Coefficients If the coefficient b1 has a nonzero value, then it is helpful in predicting the value of the response variable. If b1 = 0, it is not helpful in predicting the value of the response variable and can be eliminated from the regression equation.

To test the claim that b1 = 0 use the test statistic t = 1b1 - 02>sb1. Critical values or P-values can be found using the t distribution with n - 1k + 12 degrees of freedom, where k is the number of predictor (x) variables and n is the number of observations in the sample. The standard error sb1 is often provided by software. For example, see the accompanying StatCrunch display for Example 1, which shows that sb1 = 0.071141412 (found in the column with the heading of “Std.

Err.” and the row corresponding to the first predictor variable of height). Use the sample data in Data Set 1 “Body Data” and the StatCrunch display to test the claim that b1 = 0.

Also test the claim that b2 = 0.

What do the results imply about the regression equation?