For Exercises 72–74, use technology to solve the following problems:

  1. Verify the regression model assumptions.
  2. Construct and interpret a 95% confidence interval for .
  3. Based on the confidence interval constructed in (b), would you expect the hypothesis test to reject the null hypothesis that ?
  4. Test, at , whether a linear relationship exists between and .

Question 13.73

nutrition

73. Open the Nutrition data set. Estimate the number of calories per gram using the amount of fat per gram .

13.1.73

(a) The scatterplot of the residuals contains evidence of an unhealthy pattern and the normal probability plot indicates evidence of departures from normality in the residuals. Therefore we conclude that the regression assumptions are not verified. (b) (7.821, 8.437). We are 95% confident that the interval (13.5483, 14.6201) captures the population slope of the relationship between fat per gram and calories per gram. (c) Yes (d) . There is no relationship between fat per gram () and calories per gram . There is a linear relationship between fat per gram () and calories per gram (). Reject if . -value ≈ 0. Since the , we reject . There is evidence for a linear relationship between fat per gram () and calories per gram ().