Regression Analysis

The following regression equation was used to estimate the demand for Kroger Fruit Pies (6 independent variables - regression results on next page):

Q_it = b₀ + b₁P_it + b₂A_it + b₃P_Cit + b₄I_it + b₅Pop_it + b₆T_it + u_it

where:

Q is the quantity of pies sold during the t-th quarter,

P is the retail price in dollars of Kroger frozen pies,

A represents the dollars spent for advertising,

P_C is the price (in $) charged for competing premium-quality frozen fruit pies,

I is dollars of disposable income per capita,

Pop is the population of the market area,

T is the trend factor (tastes and preferences)

u_it is a residual (or disturbance) term

The subscript (i) indicates the regional market from which the observation was taken, whereas the subscript (t) represents the quarter during which the observation occurred.Least squares estimation of the regression equation consists of the 47 data observations resulted in the estimated regression coefficients.The results of the regression analysis statistics is shown on the next page.

A.Develop a t-test to test the statistical significance of the estimated b₃ parameter and develop the null and alternative hypothesis for this variable?Is the estimated coefficient for the competitor's price (P_C) found to be statistically significant?If found to be significant, at what level?

B.Develop a F-test to test the significance of the R² value.Include the null and alternative hypothesis for this test?If found to be significant, at what level?

Estimated Demand Function for the Kroger Gourmet Frozen Fruit Pies Variable (1) Estimated Coefficient (2) Standard Error of Coefficient (3) Computed t-statistic (4) = (2) / (3) Intercept 646,958.00 154,147.000 4.20 Price (P) -127,443.00 15,112.000 -8.43 5.35 1.114 4.80 29,337.00 12,388.000 2.37 Income (I) 0.34 3.186 0.11 Population (Pop) 0.02 0.002 10.00 Trend Factor (T) 4,406.00 4,400.000 1.00 Advertising (A) Competitor Price (Pc) Coefficient of Determination: R2 = 88.6% Adjusted R2 = 88.1% Computed F Statistic = 58.86 Standard Error of the Estimate (Total Equation) = SSE = 60,700