A manager for a large software company wants to study the factors that affect her company's sales across different regions of the US. A recently collected database contains a random sample of 135 sales regions. For each of these regions, data is available on the region's sales (Y, in dollars), the average price in that region (X1, in dollars), average marketing expenditures in that region (X2, in dollars), and the median household income level for the region (X3). Median household income level is coded as X3=0 if income level is low, and X3=1 if it is high.

The manager has several conjectures about the company's sales. Using the variable notations Y, X1, X2 and X3, you are asked to construct and interpret a regression model that enables the testing of the manager's conjectures

She conjectures that for each increase in price by 1%, sales decrease by at least $15,000. In order to enable the testing of her conjecture, the regression model has to include the following variables

Log(Y) and Log(X1)

Log(Y) and X1

Y and Log(X1)

Y and X1

None of the above

She also conjectures that for every additional dollar spent on marketing, therate of sales increaseis higher in regions with higher median household income levels. In order to enable the testing of her conjecture, the regression model has to include the following variables

X2 and X3

X2, X3 and X2*Y

X2, X3 and X3*log(Y)

X2, X3 and X2*X3

X2,X3 and log(X1)*X2

Consider the regression modelY=a+b2X2+b3X3

. Based on that model, provide a precise economic interpretation for the coefficient $b2.

For every increase in marketing expenditures by $1, sales increase/decrease by (1000)(b2).

For every increase in marketing expenditures by $1, sales increase/decrease by (100)(b2)%

For every increase in marketing expenditures by $1, sales in low median household income regions increase/decrease by (100)(b2)%

For every increase in marketing expenditures by 1%, sales in low median household income regions increase/decrease by $b2.

None of the above.

Consider the regression modelY=a+b2X2+b3X3

.The manager conjectures that sales arehigherinhighmedian household income regions. Based on this conjecture, which of the following is true:

b2=

b2>

b3 NOT EQUAL 0

b3>0

b3<0