Soft Drink Consumption. Estimate the following multiple regression models (remember that all of your independent variables will have to be in adjacent columns in Excel). Look at each set of results critically and consider how you would interpret the strengths and weaknesses of each model. Save your results from each model for use when completing the end-of-module assessment. C, the dependent variable, will always be “Consumption of Soft Drinks per Capita;” for independent variables, use the following specifications. (The notation f(X, Y, Z) means “a function of X, Y, Z; i.e., X, Y, and Z are your independent variables. Even though it isn’t listed, each model will include an intercept.) NOTE: when Excel reports a value like 2.4E-06, this is scientific notation for 2.4 * (10^-6), or 0.0000024.Model A: C = f(food services, dentists, physicians)
Model B: C = f(% obese, % smokers total)
Model C: C = f(% obese, % male smokers, % female smokers)
Model D: C = f(% obese, % smokers total, % male smokers)
Model E: C = f(mean annual temp, per capita income)
Model F: C = f(mean annual temp, per capita income, physicians)
Model G: C = f(mean annual temp, per capita income, dentists)
In model A, how much of the variation in soft drink consumption is explained by number of food service businesses, dentists, and physicians?
In model A, how would you interpret the coefficient for physicians?
a. When the number of physicians increases by 19.2%, the amount of soft drink consumption increases by 17.2%.
b. As the number of physicians per 100,000 people increases by 1, annual soft drink consumption increases by about 0.192 per year.
c. As the amount of soft drink consumption increases by 1, the amount of physicians per 100,000 people increases by 0.192.
d. As the number of physicians per 100,000 people increases by 0.192, the amount of soft drink consumption increases by 0.242.
In model A, the coefficient for number of food service businesses is statistically significant at the 5% level.
In models B through D, what seems to be the relationship between soft drink consumption and the percent who smoke?
a. As the % smokers rise, soft drink consumption increases, since all of the smoking coefficients in models B-D were positive.
b. It is difficult to describe the effect of smoking since the obese variable is insignificant in all models and thus tainting the validity of the results for the other variables.
c. It doesn’t appear that smokers (in total) is significant in model B, but separating male vs. female (in models C & D) shows that male smokers do have a significant positive effect on soft drink consumption.
d. It is difficult to draw any conclusions about male smokers because the male smoker variables were all insignificant (at the 10% level) in all models.
A state that currently has 23.5% obese adults also currently has 20% of its population who smoke (total, both male and female). The state is considering a major initiative to reduce its smoking population to 15%. If it is successful, this will also cause soft drink consumption to fall from about 160 drinks annually to about Answer drinks annually (round to nearest whole number, no decimals).
a. is shown to be positive with a relatively high degree of confidence (better than 10% significance).
b. is unimportant since, even though it was statistically significant, its coefficient estimate was always smaller in absolute value than the intercept.
c. is difficult to interpret because the smoker variables occasionally have a higher level of significance in some models than the obese variable.
d. cannot be reliably estimated since the coefficients always exceed the 10% significance level.
Of all the variables in models E through G, mean annual temperature is the only one that is statistically significant (at the 10% level).
In model A, it was seen that the dentist variable was negative and significant. In model E, the dentist variable is
a. still has a negative coefficient but is insignificant (at the 10% level).
b. even more significant since the p-value increases.
c. more important since its coefficient is less negatively related to soft drink consumption.
d. is still significant but now has a positive coefficient.
While insignificant in model A, the physicians variable is significant (at the 10% level) in model F.