Question

IBEX has hired you to analyze demand in 25 regional markets for a new Product Y, called Angelica Pickles. A statistical analysis of the demand in these markets shows (standard errors in parentheses):

QY = 250 - 10P + 6PX + 0.25A + 0.04I (100) (3) (2) (0.1) (0.15)

R2 = 90%

Standard Error of the Estimate = 75

Here, QY is the 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 $1,500, PX is $500, advertising expenditures are $50,000, and disposable income per household is $45,000. The numbers in parentheses are standard errors of the coefficients. Based on this information, do the following:

a. Calculate the expected level of demand for Y.

b. Indicate the range within which actual demand is expected to fall with 95% confidence.

c. Interpret R2.

d. Test the significance of Advertising (A), at α = 0.05.

Answer 1

QY = 250 - 10P + 6PX + 0.25A + 0.04I

Given: The price of Y is $1,500, PX is $500, advertising expenditures are $50,000, and disposable income per household is $45,000

a. E(QY)= 250 - 10P + 6PX + 0.25A + 0.04I=250-10(1500)+6(500)+0.25(50000)+0.04(45000)

E(QY)= 250-15000+3000+12500+1800=2550

b. For range the formula is:

E(QY)- (value of t from table)(Standard Error of the Estimate)2550E(QY)+ (value of t from table)(Standard Error of the Estimate)

value of t from table at 95% confidence and Degree of freedom(25-5=20): 2.086

so, range is: 2343.5525502656.45

c. Interpret R2: 90% of variation in market demand for Product Y is explained by independent variables P, A, PX, I.

d. Take

null hypothesis: coefficient of A=0 (A has no influence on QY)

alternative hypothesis: coefficient of A>0 (A has positive influence on QY)

t= (0.25-0) / 0.1= 2.5

value of t from table at LOS= 0.05 confidence and Degree of freedom(25-5=20)= 2.086

since calculated value of t is greater than critical or table value of t therefore A has positive influence on QY.