IM03b - CHAPTER 6 REGRESSION ANALYSIS ANSWERS TO PROBLEMS...

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Unformatted text preview: CHAPTER 6 REGRESSION ANALYSIS ANSWERS TO PROBLEMS AND CASES 1. Option b is inconsistent because the regression coefficient and the correlation coefficient must have the same sign. 2. a. If GNP is increased by 1 billion dollars, we will expect earnings to increase .06 billion dollars. b. If GNP is equal to zero, we expect earnings to be .078 billion dollars. 3. Correlation of Sales and AdvExpend = 0.848 The regression equation is Sales = 828 + 10.8 AdvExpend Predictor Coef SE Coef T P Constant 828.1 136.1 6.08 0.000 AdvExpend 10.787 2.384 4.52 0.002 S = 67.1945 R-Sq = 71.9% R-Sq(adj) = 68.4% Analysis of Variance Source DF SS MS F P Regression 1 92432 92432 20.47 0.002 Residual Error 8 36121 4515 Total 9 128552 a. Yes, the regression is significant. Reject : 1 = H using either the t value 2.384 and its p value .002, or the F ratio 20.47 and its p value .002. b. Y = 828 + 10.8X c. Y = 828 + 10.8(50) = $1368 d. 72% since r 2 = .719 e. Unexplained variation (SSE) = 36,121 f. Total variation (SST) is 128,552 94 4. Correlation of Time and Value = 0.967 The regression equation is Time = 0.620 + 0.109 Value Predictor Coef SE Coef T P Constant 0.6202 0.2501 2.48 0.038 Value 0.10919 0.01016 10.75 0.000 S = 0.470952 R-Sq = 93.5% R-Sq(adj) = 92.7% Analysis of Variance Source DF SS MS F P Regression 1 25.622 25.622 115.52 0.000 Residual Error 8 1.774 0.222 Total 9 27.396 a. Yes, the regression is significant. Reject : 1 = H using either the t value 10.75 and its p value .000, or the F ratio 115.52 and its p value .000. b. Y = .620 + .109X e. Unexplained variation (SSE) = 1.774 f. Total variation (TSS) = 27.396 Point forecast: Y = .620 + .1092(3) = 0.948 99% Interval forecast: Y + ts f s f = s y.x 1 1 2 2 + +-- n X X X X ( ) ( ) s f = .471 9 . 2148 ) 78 . 19 3 ( 10 1 1 2- + + = .471 131 . 1 . 1 + + = .471 231 . 1 s f = .471(1.110) = .523 .948 3.355(.523) (.807, 2.702) Prediction interval is wide because of small sample size and large confidence coefficient. Not useful. 5. a, b and d. 95 . The regression equation is Cost = 208.2 + 70.92 Age (Positive linear relationship) S = 111.610 R-Sq = 87.9% R-Sq(adj) = 86.2% Analysis of Variance Source DF SS MS F P Regression 1 634820 634820 50.96 0.000 Error 7 87197 12457 Total 8 722017 c. Correlation between Cost and Age = .938 e. Reject : 1 = H at the 5% level since F = 50.96 and its p value = .000 < .05. Could also use t = 7.14, the t value associated with the slope coefficient, and its p value = .000. The correlation coefficient is significantly different from 0 since the slope coefficient is significantly different from 0. f. Y = 208.20 + 70.92(5) = 562.80 or $562.80 6. a, b and d....
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IM03b - CHAPTER 6 REGRESSION ANALYSIS ANSWERS TO PROBLEMS...

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