2012fall-exam1-practiceproblems.pdf - ISyE4031 Regression...

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1 ISyE4031 Regression and Forecasting Practice Problems 1 Fall 2012 1. Consider the following summary quantities to estimate the parameters in a simple regression study. Assume that x and y are related according to a simple linear regression model: y = β 0 + β 1 x + ε . = - 25 1 2 ) ( i i y y = 498.96, = - 25 1 2 ) ( i i x x = 52.00, ) )( ( 25 1 y y x x i i i - - = = 160.27, y = 12.18, x =2.40 What is the estimated regression line, i.e., calculate the ordinary least squares point estimates of β 0 and β 1 ? 2. Consider the Minitab output below with several missing values. The regression equation is Y = 5 + 0.205 X Predictor Coef SE Coef T P Constant 4.9997 0.02477 201.81 0.000 X 0.2047 a 18.36 0.000 S = b R-Sq = d R-Sq(adj) = 94.6% Analysis of Variance Source DF SS MS F P Regression e 1.1138 1.1138 c 0.000 Residual Error 18 0.0595 0.0033 Total f 1.1733 a. What is the value of a ? b. What is the value of b ? 3. There is an alternate form of the simple linear regression model that is occasionally useful, i.e., the fitted model can be expressed as y ˆ = y + 1 ˆ β ( x - x ). Show that this model and the ordinary least squares estimates of the simple linear regression model, i.e., y ˆ = 0 ˆ β + 1 ˆ β x , are equivalent.
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2 4. A simple linear regression model was developed to study the relationship between the starting annual salaries of certain college graduates and their cumulative grade point averages (CGPA). Data from a group of 30 college graduates who have recently entered the job market were collected, and the following output was produced.
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