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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...

the homework document is attached, the answers for the following with work shown are required.
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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549628_STAT.xls

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