2014fall-exam1-practiceproblems.pdf

2014fall-exam1-practiceproblems.pdf - ISyE4031 Regression...

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1 ISyE4031 Regression and Forecasting Practice Problems 1 Fall 2014 1. 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 which was estimated as y ˆ = 7.6233 + 0.32964 x . y = 29.05; 2 12 1 ) ( x x i i = 6032; 2 12 1 ) ( y y i i = 835.42; a. Find xy SS . b. What is x ? c. Find the standard error, s . 2. Consider the output below with several missing values. The regression equation is Y = 646.48 14.04 X Predictor Coef SE Coef T P Constant 646.48 12.92 50.05 0.000 X -14.04 1.368 a 0.000 S = R-Sq = c R-Sq(adj) = Analysis of Variance Source DF SS MS F P Regression 18221 18221 b 0.000 Residual Error 1902.4 Total 12 20123.38 What is a ? What is b ? What is c ? 3. Consider a simple linear regression model, y = 0 + 1 x + . The ordinary least squares estimate of the slope is found to be xx xy SS SS / ˆ 1 . Prove or disprove that 2 1 1 1 ) ( ) ( ˆ x x y y x n i i n i i i . 4. Consider the following residual plots, and the Anderson-Darling test result. Answer the following True/False questions about checking the error assumptions (circle the correct answer).
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2 100 50 0 -50 99 90 50 10 1 Residual Percent 300 200 100 0 100 50 0 -50 Fitted Value Residual 75 50 25 0 -25 -50 8 6 4 2 0 Residual Frequency 18 16 14 12 10 8 6 4 2 100 50 0 -50 Observation Order Residual
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