The following regression equation was used to estimate the demandfor Kroger Fruit Pies (6 independent variables):
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,
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 on the basis of the 47 data observations resulted in the estimated regression coefficients and other statistics as shown on the following page.
A. Develop a t-test to analyze the statistical significance of the estimated parameter (b3). List the null and alternative hypotheses b3. Is the estimated coefficient for the competitor's price 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 hypothesisfor this test. If found to be significant, at what level?
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Estimated Demand Function for the
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Kroger Gourmet Frozen Fruit Pies
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Estimated
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Standard Error
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Computed
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Variable
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Coefficient
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of Coefficient
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t-statistic
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(1)
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(2)
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(3)
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(4) = (2) / (3)
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Intercept
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646,958.00
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154,147.000
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4.20
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Price (P)
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-127,443.00
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15,112.000
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-8.43
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Advertising (A)
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5.35
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1.114
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4.80
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Competitor Price (Pc)
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29,337.00
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12,388.000
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2.37
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Income (I)
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0.34
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3.186
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0.11
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Population (Pop)
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0.02
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0.002
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10.00
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Trend Factor (T)
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4,406.00
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4,400.000
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1.00
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Coefficient of Determination: R2 = 88.6%
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Adjusted R2 = 88.1%
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Computed F Statistic = 58.86
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Standard Error of the Estimate (Total Equation) = SSE = 60,700
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