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Chap12_part2

# Chap12_part2 - Solutions to End-of-Section and Chapter...

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Solutions to End-of-Section and Chapter Review Problems 47 12.75 (h) cont. E.R.A. Residual Plot -20 -15 -10 -5 0 5 10 15 0 1 2 3 4 5 6 E.R.A. Residuals Based on a visual inspection of the graphs of the distribution of the residuals versus E.R.A., there is no pattern. The model appears to be adequate. (i) p- value = 2.4201E-08 < 0.05. Reject H 0 . There is evidence that the fitted linear regression model is useful. (j) | 72.4900 79.3898 Y X μ (k) 58.1198 93.7600 I Y - (l) 1 27.2428 15.7449 β - - (m) The “population” might be considered to be all the recent years in which baseball has been played. (n) Other independent variables might be considered for inclusion in the models are (i) runs scored, (ii) hits allowed, (iii) walks allowed, (iv) number of errors, etc. 12.76 (a) Scatter Diagram 0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70 80 Sum of Ratings Price Per Person

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48 Chapter 12: Simple Linear Regression 12.76 (b) ˆ 13.6561 0.8932 Y X = - + cont. (c) Since no restaurant will receive a summated rating of 0, it is not meaningful to interpret b 0 . For each additional unit of increase in summated rating, the estimated average price per person will increase by \$0.8932. (d) ( 29 ˆ 13.6561 0.8932 50 \$31.01 Y = - + = (e) S YX = 7.0167 (f) r 2 = 0.4246. 42.46% of the variation in price per person can be explained by the variation in summated rating. (g) 2 0.4246 0.6516 r r = = = . (h) Based on a visual inspection of the residual plot of summated rating, there may be a violation of the homoscedasticity assumption. (i) p -value is virtually 0. Reject H 0 . There is very strong evidence to conclude that there is a linear relationship between price per persona and summated rating. (j) | \$29.07 \$32.94 Y X μ < < (k) \$16.95 \$45.06 I Y < < (l) 1 0.6848 1.1017 β < < (m) The linear regression model appears to have provided an adequate fit and shown a significant linear relationship between price per person and summated rating. Since 42.46% of the variation in price per person can be explained by the variation in summated rating, the summated rating is moderately useful in predicting the price. Summated rating Residual Plot -20 -15 -10 -5 0 5 10 15 20 25 0 20 40 60 80 Summated rating Residuals
Solutions to End-of-Section and Chapter Review Problems 49 12.77 (a) Scatter Plot 0 500000 1000000 1500000 2000000 2500000 3000000 3500000 4000000 4500000 0 10000 20000 30000 40000 50000 60000 Income Sales (b) 0 299876.8059 b = 1 39.1698 b = 2 299876.8059+39.1698 Y X = (c) Since median family income of customer base cannot be 0, 0 b just captures the portion of the latest one-month sales total that varies with factors other than income. 1 39.1698 b = means that as the median family income of customer base increases by one dollar, the estimated average latest one-month sales total will increase by \$39.17. (d) 849860.17 YX S = (e) 2 0.1472 r = . 14.72% of the total variation in the franchise's latest one-month sales total can be explained by using the median family income of customer base. (f) 2 0.3837 r r = = . There is not a very strong positive linear relationship between latest one-month sales total and median family income of customer base.

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50 Chapter 12: Simple Linear Regression 12.77 (g) cont. Income Residual Plot -2000000 0 2000000 0 10000 20000 30000 40000 50000 60000 Income Residuals There is a slight increase in the variance of the residuals at the higher end of the median family income. In general, however, the assumption of homoscedasticity seems to be intact. 0
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Chap12_part2 - Solutions to End-of-Section and Chapter...

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