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Spring 2010 Midterm 2 Review Slides

# Spring 2010 Midterm 2 Review Slides - Econ 203 Review 2...

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Econ 203, Review 2 Econ 203, Review 2 Andreas Hagemann April 18, 2010

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Econ 203, Review 2 Regression Output Regression I Our goal is to explain a dependent variable ( y ) by one or more independent variables ( x 1 , x 2 , . . . , x k ) such that y = β 0 + β 1 x 1 + β 2 x 2 + · · · + β k x k + ε. If we have one independent variable, this is called the simple linear regression model , and if we have more than one independent variable, we call it the multiple linear regression model . I The variable ε is called error . We don’t observe it, and therefore we make assumptions about it. I The parameter β 0 is called intercept , and the β 1 , β 2 , . . . , β k are called slope parameters. We want to estimate β 0 , β 1 , β 2 , . . . , β k .
Econ 203, Review 2 Regression Output Regression cont’d I There are two ways to write the estimated regression model: ˆ y = b 0 + b 1 x 1 + b 2 x 2 + · · · + b k x k and y = b 0 + b 1 x 1 + b 2 x 2 + · · · + b k x k + e . We refer to ˆ y as predicted value . The predicted values ˆ y are a function of the independent variables and describe the regression line (or regression plane). I The first way of writing the estimated regression model is more practical, but both ways are identical because y = ˆ y + e . I b 0 , b 1 , b 2 , . . . , b k are our estimates of β 0 , β 1 , β 2 , . . . , β k . Excel calls b 0 , b 1 , b 2 , . . . , b k coefficients . I The variable e is called residual ; it is our estimate of the unobserved error.

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Econ 203, Review 2 Regression Output Regression cont’d I We estimate the regression model by minimizing the sum of squared errors = SSE = n X i =1 e 2 i . I Another way of describing least squares regression would be so say it minimizes the sum of squared deviations of the predicted values from the dependent variable. I Recall that n is the sample size and i refers to individual observations.
Econ 203, Review 2 Regression Output Regression Statistics Multiple R 0.849 R Square 0.721 Adjusted R Square 0.709 Standard Error 7.009 Observations 50 ANOVA df SS MS F Sig. F Regression 2 5963.246 2981.623 60.70 0.0001 Residual 47 2308.762 49.123 Total 49 8272.008 Coeff. SE t Stat P-value Intercept 38.361 27.648 1.387 0.1832 x 1 -0.065 0.036 -1.796 0.0902 x 2 0.121 0.274 0.441 0.6645 I This is a typical Excel output of a multiple regression. We will work through this output step by step.

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Econ 203, Review 2 Regression Output Regression Statistics Multiple R 0.849 R Square 0.721 Adjusted R Square 0.709 Standard Error 7.009 Observations 50 ANOVA df SS MS F Sig. F Regression 2 5963.246 2981.623 60.70 0.0001 Residual 47 2308.762 49.123 Total 49 8272.008 Coeff. SE t Stat P-value Intercept 38.361 27.648 1.387 0.1832 x 1 -0.065 0.036 -1.796 0.0902 x 2 0.121 0.274 0.441 0.6645 I The regression output has 3 parts: Regression statistics , ANOVA, and regression results
Econ 203, Review 2 Regression Output Regression Statistics Multiple R 0.849 R Square 0.721 Adjusted R Square 0.709 Standard Error 7.009 Observations 50 ANOVA df SS MS F Sig. F Regression 2 5963.246 2981.623 60.70 0.0001 Residual 47 2308.762 49.123 Total 49 8272.008 Coeff. SE t Stat P-value Intercept 38.361 27.648 1.387 0.1832 x 1 -0.065 0.036 -1.796 0.0902 x 2 0.121 0.274 0.441 0.6645 I The regression output has 3 parts: Regression statistics, ANOVA , and regression results

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Econ 203, Review 2 Regression Output Regression Statistics Multiple R 0.849 R Square 0.721 Adjusted R Square 0.709 Standard Error 7.009 Observations 50 ANOVA df SS MS F Sig. F Regression 2 5963.246 2981.623 60.70 0.0001 Residual 47 2308.762 49.123 Total 49 8272.008 Coeff. SE t Stat
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Spring 2010 Midterm 2 Review Slides - Econ 203 Review 2...

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