2011fall-exam1-practiceproblems.pdf - ISyE4031 Regression...

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Group A 1 ISyE4031 Regression and Forecasting Practice Problems 1 Fall 2011 1. Short-answer questions (circle the closest correct answer ) For questions 1.1 and 1.2, consider the following summary quantities to estimate the parameters in a regression study. Assume that x and y are related according to a simple linear regression model: y ˆ = 0 ˆ β + 1 ˆ β x . SS xx = 4152.18 SS xy = 3752.09 SS yy = 3713.88 1 ˆ β = 0.9036 x = 33.4545 y = 34.06 n = 33 1.1. Calculate 0 ˆ β . a) 2.83 c) 1.11 b) 3.83 d) 0.09 1.2. Calculate SSE . a) 438.35 c) 323.49 b) 96.09 d) 121.04 1.3. Which one of the following statements is correct ? a) Regression analysis can be used to establish cause-and-effect relationships between variables. b) Suppose a fitted linear regression model is ˆ 10 2 y x = + . If x = 1 and the corresponding observed value of y = 11, the residual at this observation is - 1. c) In a linear regression model, the method of least squares results in the minimum variance estimator of a β j , however, the estimator may be biased. d) If the null hypothesis of significance of a regression H 0 : β j = 0 is rejected, we can be comfortable in concluding that the predictor j is not significant and should be rejected. 1.4. Consider a simple linear regression, y ˆ = 0 ˆ β + 1 ˆ β x . In testing the null hypothesis of significance of regression H 0 : β 1 = 0 with a t- statistic, we find that t = 4. The value of the F -statistic in the ANOVA would be: a) 4 c) 16 b) 12 d) None of the above, they are different statistics.
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Group A 2 2. Consider the Minitab output below with several missing values. (circle the closest correct answer ) The regression equation is Y = 26.8 + 1.48X Predictor Coef SE Coef T P Constant a 2.373 11.2739 0.000 X 1.4756 0.1063 b 0.000 S = 2.7004 R-Sq = c R-Sq(adj) = 88.3% Analysis of Variance Source DF SS MS F P Regression 1 1405.2 1405.2 f 0.000 Residual Error d 102.06 g
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