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The Pennsylvania State University Yao Huang Summer 2010 - Session One ASSIGNMENT 1 Due: Friday May 21 in Class Show all your work or points will be...

consider a simple regression model
The Pennsylvania State University Summer 2010 - Session One Yao Huang ASSIGNMENT 1 Due: Friday May 21 in Class Show all your work or points will be deducted. Tips: you can use Excel to complete the assignment, though the correct solution in any other package is also accepted. Make sure you provide your work. 1. Consider a simple regression model y i = β 0 + β 1 x i + u i (a) For the following data, compute the OLS estimates ˆ β 0 and ˆ β 1 estimates of parameters β 0 and β 1 ix i y i 1 1 5 2 1 2 3 2 3 4 2 3 5 2 3 6 4 2 (b) Calculate predictions ˆ Y i and residuals ˆ u i for each observation. (c) Plot the data points and estimated regression line in a graph (by hand); please indicate the residuals and predictions. 2. Suppose you have the following data on 11 student’s combined SAT scores ( X i ) and their cumulative grade point average at graduation ( Y i ). 1
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Y i X i 3 . 63 1490 2 . 37 1300 3 . 33 1510 3 . 32 1420 3 . 27 1490 2 . 37 1180 3 . 61 1550 3 . 23 1460 2 . 59 1300 3 . 30 1450 3 . 21 1550 (a) Write down the linear regression model relating X and Y . i. Calculate the following: n ; X ; Y ; n i =1 ( X i - X )( Y i - Y ); n i =1 ( X i - X ) 2 ; ˆ β 0 and ˆ β 1 ii. Calculate predictions ˆ Y i and residuals ˆ u i for each observation iii. Calculate R 2 iv. Compute n i =1 ˆ u i . Explain why do you get this result. (b) Write down the log-linear regression model relating log X and Y . i. Calculate ˆ β 0 and ˆ β 1 ii. Calculate predictions ˆ Y i and residuals ˆ u i for each observation iii. Calculate R 2 . iv. Compare two model speciFcations. Which model Fts the data better? Explain. 2
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