答案和详解如下： Q2. Which of the following reports the correct value and interpretation of the R2 for this regression? The R2 is: A) 0.048, indicating that the variability of industry sales explains about 4.8% of the variability of company sales. B) 0.952, indicating that the variability of industry sales explains about 95.2% of the variability of company sales. C) 0.952, indicating the variability of company sales explains about 95.2% of the variability of industry sales. Correct answer is B) The R2 = (SST − SSE) / SST = (12,500 − 600.50) / 12,500 = 0.952 The interpretation of this R2 is that 95.2% of the variation in company XYZ's sales is explained by the variation in tissue industry sales. Q3. What is the predicted value for sales of Company XYZ given industry sales of $3,500? A) $994.88. B) $900.00. C) $883.72. Correct answer is C) The regression equation is Y = (−94.88) + 0.2796 × X = −94.88 + 0.2796 × (3,500) = 883.72. Q4. What is the upper limit of a 95% confidence interval for the predicted value of company sales (Y) given industry sales of $3,300? A) 877.13. B) 827.87. C) 318.42. Correct answer is A) The predicted value is Ŷ = −94.88 + 0.2796 × 3,300 = 827.8. The upper limit for a 95% confidence interval = Ŷ + tcsf = 827.8 + 3.182 × 15.5028 = 827.8 + 49.33 = 877.13 (Interim calculations below). The critical value of tc at 95% confidence and 3 degrees of freedom is 3.182. The standard error of the forecast, sf2= se2[1 + 1/n + (X − X)2/(n - 1)sx2], where se2 = MSE = 200.17
n = 5
X = 3,300
X = 16,450 / 5 = 3,290
sx2 = Σ(Xi − X)2 / (n - 1) = 152,000 / 4 = 38,000 Substituting, sf2 = 200.17 × {1 + 1/5 + (3,300 – 3,290)2 / [(5 - 1) × 38,000]} = 240.335691. sf = 15.5028 | 
发表于 2009-1-7 14:12
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