Burning calories with exercise. Many exercise bikes, elliptical trainers, and treadmills display basic information like distance, speed, calories burned per hour (or total calories), and duration of the workout. Let's take another look at the data in Table 28.9 (page 28-63) that were used for the Check Your Skills exercises. Scatterplots show different linear relationships for each incline, one for slow speeds and another for faster speeds, so the following indicator variables were created:
Below is part of the Minitab output from fitting a multiple regression model to predict Calories from Mph, IndSlow, NoIncline, and 2%Incline for the Cybex.
(a) Use the Minitab output to estimate each parameter in this multiple regression model for predicting calories burned with the Cybex machine. Don't forget to estimate σ.
(b) How many separate lines are fitted with this model? Do the lines all have the same slope? Identify each fitted line.
(c) Do you think that this model provides a good fit for these data? Explain.
(d) Is there significant evidence that more calories are burned for higher speeds? State the hypotheses, identify the test statistic and P-value, and provide a conclusion in the context of this question.
