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Consider a simple regression model




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 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;yi = 0 + 1 xi + ui;(a) For the following data, compute the OLS estimates 0 and 1 estimates of;parameters 0 and 1;i;xi;yi;1;1;5;2;1;2;3;2;3;4;2;3;5;2;3;6;4;2;(b) Calculate predictions Yi and residuals ui 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 students combined SAT scores (Xi);and their cumulative grade point average at graduation (Yi).;1;Yi;Xi;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=1 (Xi X)(Yi Y), n=1 (Xi X)2;i;i;0 and 1;ii. Calculate predictions Yi and residuals ui for each observation;2;iii. Calculate R;iv. Compute n=1 ui. Explain why do you get this result.;i;(b) Write down the log-linear regression model relating log X and Y.;i. Calculate 0 and 1;ii. Calculate predictions Yi and residuals ui for each observation;iii. Calculate R2.;iv. Compare two model specications. Which model ts the data better?;Explain.;2


Paper#22496 | Written in 18-Jul-2015

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