Use the following data set for Exercises 21-26.

0.6 1 10 1.3
4.0 2 10 −3.2
3.2 3 8 −1.0
9.0 4 8 0.9
1.8 5 6 −2.5
8.4 6 6 0.9
9.8 7 4 1.0
10.4 8 4 2.0
8.8 9 2 0.2
14.7 10 2 −2.2

Question 13.125

23. Perform the test for the significance of the individual predictor variables, using level of significance . Do the following:

  1. For each hypothesis test, state the hypotheses and the rejection rule.
  2. For each hypothesis test, find the statistic and the -value.
  3. For each hypothesis test, state the conclusion and interpretation.

13.3.23

(a) Test : There is no linear relationship between and . : There is a linear relationship between and . Reject if the -value . Test 2: : There is no linear relationship between and . : There is a linear relationship between and . Reject if the -value . Test 3: : There is no linear relationship between and . : There is a linear relationship between and . Reject if the -value . (b) Test , with . Test , with . Test , 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 . Test 3: The , which is not . Therefore we do not reject . There is insufficient evidence of a linear relationship between and .