Solution to Tutorial 1 - Solutions to Tutorial Questions 1...

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Unformatted text preview: Solutions to Tutorial Questions 1 1. For model Y i = β + β 1 X i + ε i assume that X = 0 is within the scope of the model. What is the implication for the regression function Y i = β + β 1 X i if β = 0 so that the model is Y i = β 1 X i + ε i ? How would the regression function Y i = β + β 1 X i plot on the graph? [hint: what is the interpretation of β ] The intercept is 0, indicating when X i = 0 the expected value of Y i is 0. The plot will pass through the origin (0,0). 2. Refer to the regression model above, what is the implication for the regression function if β 1 = 0 so that the model is Y i = β + ε i ? How would the regression function Y i = β + β 1 X i plot on the graph? [hint: what is the interpretation of β 1 ] The slop is 0, indicating when X i increases Y i dones not change linearly. The plot will be a horizontal line passing through (0 , b ). Statistically, X has no linear relation with Y . 3. (Grade Point average): For graduate students, X is ACT test score, Y is GPA. There are 120 students, and their ACT and GPA are recorded. The data can be found at (dataTutorial1a.dat) . Suppose we predict Y based on X by a simple linear regression model above. (a) Obtain the LSE of β and β 1 (b) plot the estimated regression function and the data. Does the estimated regression appear to ±t the data well? (b) plot the estimated regression function and the data....
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This note was uploaded on 10/04/2010 for the course STAT ST3131 taught by Professor Xiayingcun during the Fall '09 term at National University of Singapore.

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Solution to Tutorial 1 - Solutions to Tutorial Questions 1...

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