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### Exam2

Course: XLZT 2006, Fall 2009
School: Maryville MO
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Word Count: 656

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2 Exam (100pts) Stat 3500 (W06) Instructor: Lin, Xiaoyan Name:________________ Section: _________ Note: please show all of your work to get partial credit. Good luck! Note: during your intermediate steps of calculation, you'd better keep at least 3 decimal digits. 1. (40pts) Suppose you are a manufacturer who wants to obtain a quality measure on a product, but the procedure to obtain the measure is expensive....

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2 Exam (100pts) Stat 3500 (W06) Instructor: Lin, Xiaoyan Name:________________ Section: _________ Note: please show all of your work to get partial credit. Good luck! Note: during your intermediate steps of calculation, you'd better keep at least 3 decimal digits. 1. (40pts) Suppose you are a manufacturer who wants to obtain a quality measure on a product, but the procedure to obtain the measure is expensive. There is an indirect approach, which uses a different product score (Score 1) in place of the actual quality measure (Score 2). This approach is less costly but also is less precise. You can use simple linear regression analysis to see if Score 1 explains a significant amount of variation in Score 2 to determine if Score 1 is an acceptable substitute for Score 2. The regression analysis is based on the following 9 products. Score 1, x 4.1 Score 2, y 2.1 2.2 2.7 1.5 1.7 6.0 2.5 8.5 3.0 4.1 2.1 9.0 3.2 8.0 2.8 7.5 2.5 SSyy = 2.656, SSxx =53.649, SSxy =11.678 a). (10pts) Calculate MSE, that is, s2. b). (6pts) Regardless of your answer to part a, assume MSE=0.0162. Compute the estimated standard error of the model, s . 1 c). (5pts) Interpret your answer to part b in the context of the problem. d). (11pts) Regardless of your answer to part b, take the estimated standard error of the model to be 0.127. Calculate a 95% interval for the slope to see if there is really a relationship between Score 1 and Score 2. Be sure to explain why there is or is not a relationship. e). (8pts) Calculate the proportion of variation in Score 2 that is explained by Score 1 using the least squares line. 2 2. (42pts) Economic theory suggests that wages and quit rates are related. The theory is that the quit rate (y, quits per 100 employees) decreases as the average hourly wage(x, \$) increases. Use the output below to answer the following questions (Note: a sample of 15 manufacturing industries is used to do the analysis.) Predictor Constant x S = _____ Coef 4.8615 -0.3466 SE Coef 0.5201 0.0587 T 9.35 ____ P 0.000 0.000 R-Sq = _______ R-Sq(adj) = 70.8% Analysis of Variance Source Regression Residual Error Total DF 1 13 14 SS 8.2507 MS 8.2507 3.0733____________ 11.3240 F 34.90 P 0.000 a). (6pts) Write out the least squares line. b). (16pts)Assume that the assumptions about model hold, conduct a test to determine if there is really a negative relationship between the average hourly wage and the quit rate. Use =.05. Ho: Ha : Test Statistic: Decision Rule ( use t-statistic or p-value): Conclusion & Interpretation: 3 c.) (10pts) Assuming that the assumptions about model hold, use the least squares (regression) line to form a 95% interval for estimating the mean quit rate for all industries with an average hourly wage of \$9.00. Assume SSxx =68.70, x = 9.00. Interpret this result. d.) (10pts) Assuming that the assumptions about model hold, use the least squares (regression) line to form a 95% interval for the quit rate in an industry with an average hourly wage of \$9.00. Assume SSxx =68.70, x = 9.00. Interpret this result. 3. (18pts) Multiple Choice. Circle the one alternative that best completes the statement or answer the question. 1) If you were asked to see if there is really a relationship between two variables, then which one of the following you would do? A) B) C) D) Conduct a hypothesis test for the slope Construct a prediction interval for the slope Conduct a hypothesis test for the y-intercept Both A and C 4 2) If the least squares line perfectly fits the data points, then which of the following is true? A) B) C) D) The coefficient of determination is 1. The correlation coefficient is 1 or -1. Both A and B The value of the slope is 1 3) When r= -.83, then ^ ^ A) 1 <0 B) 1 =0 ^ C) 1 >0 ^ D) know nothing about 1 4) Which correlation coefficient exhibits the strongest linear relationship between two variables? A) r= -.56 B) r=.80 C) r=.-87 D) r=.20 5) The constant variance assumption is met when there is ____ for the graph of the residuals versus the fitted values. A) a detectable pattern B) no noticeable pattern 6) Suppose we do the regression analysis to make prediction, which of the following x p 's has the narrowest prediction interval? Assume x = 8.0. A) x p =7.5 B) x p =8.8 C) x p =8.0 D) x p =9.2 5
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