9.
With milk sales sagging of late, The Milk Processor Education Program (MPEP)
decided to move on from the famous "Got Milk" ad slogan in favor of a new
one, "Milk Life." The new tagline emphasizes milk's nutritional benefits,
including its protein content. MPEP began collecting data on the number of
gallons of milk households consumed weekly (in millions), weekly price per
gallon, and weekly expenditures on milk advertising (in hundreds of dollars)
for the period following the launch of the new campaign. These data, in
forms to estimate both a linear model and log-linear model, are available via
the link below. Use these data to perform two regressions: a linear
regression and a log-linear regression.
Excel Data File
Which model does a better job fitting the data?
The linear model.
Suppose that the weekly price of milk is $3.40 per gallon and MPEP decides
to ramp up weekly advertising by 35 percent to $150 (in hundreds). Use the
best-fitting regression model to estimate the weekly quantity of milk
consumed after this advertising increase.
Instructions: Round your intermediate calculations and enter your response
rounded to three decimal places.
1.796 ± 0.1 million gallons per week
2
Explanation
For the linear regression model, the estimates indicate that R = .55, or that 55 percent
of the variability in the quantity demanded is explained by price and advertising. In
contrast, the R2 for the log-linear model is .40, indicating that only 40 percent of the
variability in the natural log of quantity is explained by variation in the natural log of
price and the natural log of advertising. Therefore, the linear regression model appears
to do a better job explaining variation in the dependent variable. This conclusion is
further supported by comparing the adjusted R2s and the F-statistics in the two models.
In the linear regression model the adjusted R2 is greater than in the log-linear model: .
54 compared to .39, respectively. The F-statistic in the linear regression model is 58.61,
which is larger than the F-statistic of 32.52 in the log-linear regression model. Taken
together these three measures suggest that the linear regression model fits the data
better than the log-linear model.
At P = $3.40 and A = $150, milk consumption is 1.796 million gallons per week: Qdmilk =
6.52 - 1.61(3.40) + 0.005(150) = 1.796.
