Case-1: Regression Statistics. June Ward, controller fo…
Case-1: Regression Statistics. June Ward, controller for NAFTA, Inc., has asked you to analyze demand in 30 regional markets for Beaver’s Cleavers, a new brush cutting d service, dubbed Product Y. A statistical analysis of demand in these markets shows (standard errors in parentheses): QY = 2,000 – 25P + 10PX + 0.025I (1,500) (8) (4) (0.011) R2 = 80% F = 34.7 Standard Error of the Estimate = 40 Here, QY is 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 $100, PX is $50, and disposable income per family averages $80,000. In order to answer the question, you need to use the following table with critical values for the F-distribution: Table 1: Critical Values for F-distribution at 10% Level of Significance Numerator Degrees of Freedom 1 2 3 4 5 6 7 8 9 10 Denominator Degrees of Freedom 10 3.29 2.92 2.73 2.61 2.52 2.46 2.41 2.38 2.35 2.32 11 3.23 2.86 2.66 2.54 2.45 2.39 2.34 2.30 2.27 2.25 12 3.18 2.81 2.61 2.48 2.39 2.33 2.28 2.24 2.21 2.19 13 3.14 2.76 2.56 2.43 2.35 2.28 2.23 2.20 2.16 2.14 30 2.88 2.49 2.28 2.14 2.05 1.98 1.93 1.88 1.85 1.82 120 2.75 2.35 2.13 1.99 1.90 1.82 1.77 1.72 1.68 1.65 More than 120 2.71 2.30 2.08 1.94 1.85 1.77 1.72 1.67 1.63 1.60 Table 2: Critical Values for F-distribution at 5% Level of Significance Numerator Degrees of Freedom 1 2 3 4 5 6 7 8 9 10 Denominator Degrees of Freedom 10 4.96 4.10 3.71 3.48 3.33 3.22 3.14 3.07 3.02 2.98 11 4.84 3.98 3.59 3.36 3.20 3.09 3.01 2.95 2.90 2.85 12 4.75 3.89 3.49 3.26 3.11 3.00 2.91 2.85 2.80 2.75 13 4.67 3.81 3.41 3.18 3.03 2.92 2.83 2.77 2.71 2.67 30 4.17 3.32 2.92 2.69 2.53 2.42 2.33 2.27 2.21 2.16 120 3.92 3.07 2.68 2.45 2.29 2.17 2.09 2.02 1.96 1.91 More than 120 3.84 3.00 2.60 2.37 2.21 2.10 2.01 1.94 1.88 1.83 Table 3: Critical Values for F-distribution at 1% Level of Significance Numerator Degrees of Freedom 1 2 3 4 5 6 7 8 9 10 Denominator Degrees of Freedom 10 10.04 7.56 6.55 5.99 5.64 5.39 5.20 5.06 4.94 4.85 11 9.65 7.21 6.22 5.67 5.32 5.07 4.89 4.74 4.63 4.54 12 9.33 6.93 5.95 5.41 5.06 4.82 4.64 4.50 4.39 4.30 13 9.07 6.70 5.74 5.21 4.86 4.62 4.44 4.30 4.19 4.10 30 7.56 5.39 4.51 4.02 3.70 3.47 3.30 3.17 3.07 2.98 120 6.85 4.79 3.95 3.48 3.17 2.96 2.79 2.66 2.56 2.47 More than 120 6.63 4.61 3.78 3.32 3.02 2.80 2.64 2.51 2.41 2.32 Based on the F test, we can conclude the following about the overall significance of the regressions results:
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