Testing Hypotheses About Regression Coefficients If the coefficient 1 has a nonzero

Chapter 10, Problem 17

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Testing Hypotheses About Regression Coefficients If the coefficient 1 has a nonzero value, then it is helpful in predicting the value of the response variable. If 1 = 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 1 = 0 use the test statistic t = ( b 1 0 ) / s b 1 . Critical values or Pvalues 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 s b 1 is often provided by software. For example, the Minitab display in Example 1 shows that s b 1 = 0.1289 (found in the column with the heading of SE Coeff and the row corresponding to the first predictor variable of the height of the mother). Use the sample data in Table 104 and the Minitab display in Example 1 to test the claim that 1 = 0 . Also test the claim that 2 = 0 . What do the results imply about the regression equation?