Let us return once more to the body-mass index (BMI) example for the BRFSS data. We now extend the models involving the explanatory factors of drinking frequency, age, and sleep quality in Chapters 8-9 to consider a model that includes all first-order product terms involving these three factors. Selected output for both models is provided below.
a. Perform and interpret a hypothesis test that evaluates the presence of interaction in this model.
b. If the main interest is to understand the relationship between drinking frequency and BMI, based on results obtained in Section 5.12, is controlling for age and sleep quality necessary?
c. A researcher believes that sleep quality should be controlled for given the results of the hypothesis test shown below. Do you agree with this assessment? What would you say to this researcher?

Regression of BMI on DRINK DAYS, AGE, POOR SLEEP DAYS, with 2-way interactions DF Sum of Squares Mean Square FValue Pr> F Source Modal Error Corrected Total 6.81 0001 1409 32009 1042 35945 73599 1048 37355.05608 234 88668 34.49687 Portion of output omitted Type I SS F Value PrF Source drink days AGE poor sleep days drink days AGE drink days poor sleep AGE poor sleep days DF Mean Square 11073.403915 11.595517 204.794319 917524 8.581905 106.026909 1073 403915 11.595517 204.794319 4.917524 8.581905 106.026909 31.12 0001 0.34 0.5622 5.94 0 0150 0.14 0.7058 025 0.6180 3.07 0.0799 Regression of BMI on DRINK DAYS, AGE, POOR SLEEP DAYS Portion of output omitted Mean Square FVtue Pr> F Source drink days AGE poor sleep days DF Type ISS 1073 403915 11.595517 204.794319 1073.403915 11.595517 204 794319 31.10 0001 0.34 0.5623 5.93 0.0150 [Portion of output omitted Estimate Standard Error t Value PrI Parameter Intercept drink days AGE poor sleep days 26 66350677 0.70642133 37.74