Section V$.(23$pt$.)$

$$

$$

$$Wharton Econometric Forecasting, LLC has been hired to analyze demand in $30$ regional markets for Product Y$,$ a major item. A statistical analysis of demand in these markets shows $($standard errors in parentheses$)$:

$$

$$ QY $=26,950440$P $+220$PX $+0\mathrm{.}08$A $+0\mathrm{.}01$I

$(11,000)(150)(180)(0\mathrm{.}3)(0\mathrm{.}05)$

$$

$$ R$2=0\mathrm{.}95$

$$

Standard Error of the Estimate $=12$

$$

Here, QY is market demand for Product Y$,$ P is the price of Y in dollars, A is dollars of advertising expenditures, PX is the average price in dollars of another $($unidentified$)$ product, and I is dollars of household income. In a typical market, the price of Y is $$100,$ PX is $$60,$ advertising expenditures are $$50,000,$ and average family income is $$60,000.$

$$

A$.(4$ pt$.)$ Use the estimated demand function to calculate the expected value of QY in a typical market.

B$.(5$ pt$.)$ Calculate the $95\%$ confidence interval within which you would expect to find actual values of sales.

C$.(5$ pt$.)$ Calculate the point price elasticity of demand, advertising point elasticity, and cross$-$price point elasticity.

D$.(4$ pt$.)$ Would a reduction in price result in an increase in total revenues? Why? or Why not?

E$.(5$ pt$.)$ Which variables in this regression model are statistically significant at the $95$percent confidence level? Show your work.