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Solutions to assignment #1 questions related to regression analysis. Topics covered include functional relationships, population and observed responses, least squares method, and confidence intervals. The document also includes minitab output for reference.

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Download Chapter 1 and 2 Assignment Solutions: Regression Analysis and more Assignments Statistics in PDF only on Docsity! Assignment #1 Solutions Chapter 1 2. The relation is a functional (or deterministic relationship): Y = 300 + 2X. 5. The student is incorrect. The population relationship is described by µY = E (Y ) = β0 + β1X. There is no error, εi, when you consider the population relationship. The error only occurs when you sample from the population. Then, the observed response, Yi, can be considered a function of some trend (β0 + β1X) and some error (εi). That is, Yi = β0 + β1X + εi. 8. Based on the relationship described in Figure 1.6, the mean (or expected) number of hours to prepare X = 45 bids is 104. Therefore, for X = 45 bids, we say that every observed response, Yi, comes from a population with mean µY = E (Y ) = 104. That is, we say E (Yi) = 104 when X = 45. It is unlikely that it would take exactly 108 hours the next time they prepared 45 bids. 16. The least squares method is valid regardless of how the responses (or errors) are distributed (see page 29). (However, the t-tests and confidence intervals we learned for β0 and β1 do depend on the assumption that the responses (or errors) are normally distributed. It’s no big deal if the responses deviate only slightly from normality. With large data sets, the deviation from normality can even be quite large.) 17. The statement is inappropriate. The values b0 and b1 don’t need to be estimated; they can be calculated directly from the sample data. It’s the regression parameters β0 and β1 that we estimate by the least squares method. 19. The Minitab output to help answer this question is: The regression equation is cgpa = - 1.70 + 0.840 score Predictor Coef SE Coef T P Constant -1.6996 0.7268 -2.34 0.031 score 0.8399 0.1440 5.83 0.000 S = 0.4350 R-Sq = 65.4% R-Sq(adj) = 63.5% Analysis of Variance Source DF SS MS F P Regression 1 6.4337 6.4337 34.00 0.000 Residual Error 18 3.4063 0.1892 Total 19 9.8400 a. The least squares estimates, b0 and b1, are -1.70 and 0.84, respectively. b. Figure 1 contains a fitted line plot. There is still quite a bit of scatter, but a linear regression function does appear to describe the general trend fairly well. c. The mean freshman GPA for students with an entrance test score of X = 5.0 is −1.7 + 0.84 (5) = 2.5. d. The estimated slope quantifies this amount. That is, the estimated change in the mean response when the entrance test score increases by one point is 0.84. Chapter 2 4. To help answer this question, see the Minitab output from question 19 in chapter 1. 1