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 = (b1 - 0)>sb1.

Critical values or P-values can be found using the t distribution with n - (k + 1) 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, the Excel display in Example 1 shows that s = 0.1289 (found in the column with the heading of Standard Error and the row corresponding to the first predictor variable of the height of the mother). Use the sample data in Table 4 and the Excel display in Example 1 to test the claim that b1 = 0.

Also test the claim that b2 = 0.

What do the results imply about the regression equation?