Under econometrics prof keunkwan ryu 8 some rules of

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Under Econometrics Prof. Keunkwan Ryu 8 Some Rules of Thumb What types of variables are often used in log form? Dollar amounts that must be positive Very large variables, such as population What types of variables are often used in level form? Variables measured in years Variables that are a proportion or percent
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Fall 2008 Under Econometrics Prof. Keunkwan Ryu 9 Quadratic Models For a model of the form y = β 0 + β 1 x + β 2 x 2 + u we can’t interpret β 1 alone as measuring the change in y with respect to x , we need to take into account β 2 as well, since ( 29 x x y x x y 2 1 2 1 ˆ 2 ˆ ˆ so , ˆ 2 ˆ ˆ β β β β + +
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Quadratic relationship Fall 2008 Under Econometrics Prof. Keunkwan Ryu 10
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Quadratic relationship Fall 2008 Under Econometrics Prof. Keunkwan Ryu 11
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Fall 2008 Under Econometrics Prof. Keunkwan Ryu 12 More on Quadratic Models Suppose that the coefficient on x is positive and the coefficient on x 2 is negative Then y is increasing in x at first, but will eventually turn around and be decreasing in x ( 29 2 1 * 2 1 ˆ 2 ˆ at be will point turning the 0 ˆ and 0 ˆ For β β β β = < x
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Fall 2008 Under Econometrics Prof. Keunkwan Ryu 13 More on Quadratic Models Suppose that the coefficient on x is negative and the coefficient on x 2 is positive Then y is decreasing in x at first, but will eventually turn around and be increasing in x ( 29 0 ˆ and 0 ˆ when as same the is which , ˆ 2 ˆ at be will point turning the 0 ˆ and 0 ˆ For 2 1 2 1 * 2 1 < = < β β β β β β x
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Fall 2008 Under Econometrics Prof. Keunkwan Ryu 14 Interaction Terms For a model of the form y = β 0 + β 1 x 1 + β 2 x 2 + β 3 x 1 x 2 + u we can’t interpret β 1 alone as measuring the change in y with respect to x 1 , we need to take into account β 3 as well, since 2 1 2 3 1 1 at above the evaluate typically we on of effect the summarize to so , x y x x x y β β + =
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Fall 2008 Under Econometrics Prof. Keunkwan Ryu 15 Adjusted R -Squared Recall that the R 2 will always increase as more variables are added to the model The adjusted R 2 takes into account the number of variables in a model, and may decrease ( 29 [ ] ( 29 [ ] ( 29 [ ] 1 ˆ 1 1 1 1 2 2 - - = - - - - n SST n SST k n SSR R σ
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Fall 2008 Under Econometrics Prof. Keunkwan Ryu 16 Adjusted R -Squared (cont) It’s easy to see that the adjusted R 2
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