Use the following data set for Exercises 27–33. Note that is a dummy variable.
| −0.7 | 2 | 0.1 | 0 |
| 6.4 | 4 | −2.5 | 1 |
| 2.8 | 6 | 2.7 | 0 |
| 9.4 | 8 | 2.8 | 1 |
| 8.6 | 10 | −1.6 | 0 |
| 13.1 | 12 | 1.0 | 1 |
| 12.2 | 14 | −1.4 | 0 |
| 19.1 | 16 | −0.5 | 1 |
| 18.8 | 18 | 1.0 | 0 |
| 23.2 | 20 | −2.3 | 1 |
31. Identify any predictors that have corresponding -values greater than the level of significance . Of these, discard the variable with the largest -value. Then redo Exercise 30, omitting this predictor. Repeat if necessary.
13.3.31
The -value for is the only -value greater than , so we eliminate from the multiple regression equation. The new regression equation is . (a) Test : There is no linear relationship between and . : There is a linear relationship between and . Reject if the -value . Test There is no linear relationship between and . : There is a linear relationship between and . Reject if the -value . (b) Test 1: , with ; Test 2: , with . (c) Test 1: The , which is . Therefore we reject . There is evidence of a linear relationship between and . Test 2: The , which is . Therefore we reject . There is evidence of a linear relationship between and . Since all of the variables are significant, we have our final multiple regression equation.