Question
The following regression equation was used to estimate the demand for Kroger Fruit Pies (6 independent variables - regression results on next page): Q it
The following regression equation was used to estimate the demand for Kroger Fruit Pies (6 independent variables - regression results on next page):
Qit = b0 + b1Pit + b2Ait + b3PCit + b4Iit + b5Popit + b6Tit + uit
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,
PC 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)
uit 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 (PC) 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
Estimated
Standard Error
Computed
Variable
Coefficient
of Coefficient
t-statistic
(1)
(2)
(3)
(4) = (2) / (3)
Intercept
646,958.00
154,147.000
4.20
Price (P)
-127,443.00
15,112.000
-8.43
Advertising (A)
5.35
1.114
4.80
Competitor Price (Pc)
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
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
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