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Unformatted text preview: Stat 104: Quantitative Methods for Economists Class 33: Regression Diagnostics 1 The Model and Data Y X = + + 1 Given X s X X X m 1 2 , , K We assume the following model holds: 2 ~ (0, ) i N independent Y X i i i = + + 1 2 3 2 1 50 40 30 20 price Given data size We ( hope, assume ) we see a linear pattern and a level of variation about the line. Our model is designed to capture these two features of the data. 3 In practice we need to check our assumption that the model captures the important features of the data. Is the model a good way to describe the data?? This is called model checking, and is done using the residuals from the regression. 4 Why do we have to check our model? s All estimates, intervals, and hypothesis tests have been developed assuming that the model is correct. s If the model is incorrect, then the formulas and methods we use are at risk of being incorrect. 5 To drive this point home, lets look at the famous Anscomb data sets 6 Data Set 1 y1 = 3.00 + 0.500 x1 Predictor Coef SE Coef T P Constant 3.000 1.125 2.67 0.026 x1 0.5001 0.1179 4.24 0.002 s = 1.237 Rsq = 66.7% Rsq(adj) = 62.9% Analysis of Variance SOURCE DF SS MS F p egression 7 10 7 10 7 9 02 14 9 4 11 10 9 8 7 6 5 4 x 1 y1 Regression 1 27.510 27.510 17.99 0.002 Error 9 13.763 1.529 Total 10 41.273 7 Data Set 2 y2 = 3.00 + 0.500 x2 Predictor Coef SE Coef T P Constant 3.001 1.125 2.67 0.026 x2 0.5000 0.1180 4.24 0.002 s = 1.237 Rsq = 66.6% Rsq(adj) = 62.9% Analysis of Variance SOURCE DF SS MS F p Regression 1 27.500 27.500 17.97 0.002 14 9 4 9 8 7 6 5 4 3 x 2 y 2 Error 9 13.776 1.531 Total 10 41.276 8 Data Set 3 y3 = 3.00 + 0.500 x3 Predictor Coef SE Coef T P Constant 3.002 1.124 2.67 0.026 x3 0.4997 0.1179 4.24 0.002 s = 1.236 Rsq = 66.6% Rsq(adj) = 62.9% Analysis of Variance SOURCE DF SS MS F p Regression 1 27.470 27.470 17.97 0.002 Error 9 13.756 1.528 Total 10 41.226 14 9 4 13 12 11 10 9 8 7 6 5 x 3 y 3 9 Data Set 4 y4 = 3.00 + 0.500 x4 Predictor Coef SE Coef T P Constant 3.002 1.124 2.67 0.026 x4 0.4999 0.1178 4.24 0.002 s = 1.236 Rsq = 66.7% Rsq(adj) = 63.0% Analysis of Variance SOURCE DF SS MS F p egression 7 90 7 90 8 02 Regression 1 27.490 27.490 18.00 0.002 Error 9 13.742 1.527 Total 10 41.232 2 0 15 10 13 12 11 10 9 8 7 6 5 x 4 y 4 10 Anscomb Conclusion ? s No data is bad; it just might not meet your assumptions. The data could simply be naughty. your assumptions arent met, the computer s If your assumptions arent met, the computer output might appear perfectly reasonable, but in reality be uninterpretable....
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 Fall '11
 MichaelParzen

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