Question

According to CNN, two dairy farmers challenged the legality of the funding of the “Got Milk?” campaigns. They argued that the “Got Milk?” campaigns do little to support milk from cows that are not injected with hormones and other sustainable agriculture products, and therefore violate their (and other farmers’) First Amendment rights. The third U.S. Circuit Court of Appeals agreed and concluded that dairy farmers cannot be required to pay to fund the advertising campaigns. One of the obvious backlashes to the National Dairy Promotion and Research Board is reduced funding for advertising campaigns. To assess the likely impact on milk consumption, suppose that the National Dairy Promotion and Research Board collected 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). These data, in forms to estimate both a linear model and log-linear model, are available online at www.mhhe.com/baye8e in a file named Q20.xls. Use these data to perform two regressions: a linear regression and a log-linear regression. Compare and contrast the regression output of the two models. Comment on which model does a better job fitting the data. Suppose that the weekly price of milk is $\mathbf{\backslash (}\mathbf{3}\mathbf{.}\mathbf{40}$per gallon and the National Dairy Promotion and Research Board’s weekly advertising expenditures fall$\mathbf{35}$percent after the court’s ruling to $\mathbf{\backslash )}\mathbf{150}$ (in hundreds). Use the best-fitting regression model to estimate the weekly quantity of milk consumed after the court’s ruling.

Short answer

The weekly quantity of milk consumed after the court's ruling is 61.03 gallons.

Step-by-step solution

The regression analysis

As per the above data, the log-linear regression equation can be interpreted as:

$Q_x^d=a+b{P}_x+c{A}_x$

Find weekly quantity of milk consumed

Reading the value of coefficients we obtain the estimated linear model function:

$Q_x^d=6.52-1.614P_x+0.004A_x$

Here,

$Q_x^d$is the demand for milk

$P_x$is the price of milk in gallons

$A_x$is the price of milk advertising

Assuming now that the weekly price of milk is$3.40$per gallon and that the weekly cost of the Advertising Board is $15,000$.

By substituting the given values into the equation of the linear regression model, we will get an estimate weekly amounts of milk consumed.

Therefore,

$Q_x^d=6.52-1.614P_x+0.04A_x$

$$\begin{gathered} Q_x^d=6.52-1.614·3.4+0.004·15,000 \\ {Q}_x^d=6.52-5.49+60 \\ {Q}_x^d=61.03 \end{gathered}$$

Thus, the weekly quantity of milk consumed after the court's ruling is localid="1658333192373" $\mathbf{61}\mathbf{.}\mathbf{03}$gallons.