The article “Promoting Healthy Choices: Information versus Convenience” (Amer. Econ. J.: Appl. Econ. 2010: 164–178) reported on a field experiment at a fast-food sandwich chain to see whether calorie information provided to patrons would affect calorie intake. One aspect of the study involved fitting a multiple regression model with seven predictors to data consisting of 342 observations. Predictors in the model included age and indicator variables for sex, whether or not a daily calorie recommendation was provided, and whether or not calorie information about choices was provided. The reported value of the F ratio for testing model utility was 3.64.
a. At significance level .01, does the model appear to specify a useful linear relationship between calorie intake and at least one of the predictors?
b. What can be said about the P-value for the model utility F test?
c. What proportion of the observed variation in calorie intake can be attributed to the model relationship? Does this seem very impressive? Why is the P value as small as it is?
d. The estimated coefficient for the indicator variable calorie information provided was −71.73, with an estimated standard error of 25.29. Interpret the coefficient. After adjusting for the effects of other predictors, does it appear that true average calorie intake depends on whether or not calorie information is provided? Carry out a test of appropriate hypotheses.