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321_09_slides9 - Further Issues Chapter 6 Econ 321...

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Further Issues Chapter 6  Econ 321  Introduction to Econometrics Econ 321-Stéphanie Lluis 1
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Outline Data scaling More on functional forms Residual analysis More on Goodness of fit More on the effect of adding regressors Interaction effects Econ 321-Stéphanie Lluis 2
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Effect of Scaling Data Econ 321-Stéphanie Lluis 3
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Residual Analysis A) Use the residuals to examine individual  observations compare the actual values of the dependent  variable with the predicted one B) Use the residuals to examine their  behaviour graphically  distribution (normality assumption) As a function of y (functional form) As a function of x i  (heteroscedasticity) Econ 321-Stéphanie Lluis 4
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A-Individual Residuals Econ 321-Stéphanie Lluis 5
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6 B-Residuals from Levels  Regression Residuals from a regression of Weekly Earnings on demographic characteristics Skewed to the right
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7 B-Residuals from Log  Regression Residuals from a regression of Log Weekly Earnings on demographic characteristics Almost symmetrical —use of t distribution is probably OK
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B-Which Functional Form? X Y Are there  Outliers or  should we use  a quadratic  form? Diagnostic plot of the residuals
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B-Diagnostic Plot of Residuals Normal Diagnostic Plot Predicted Values Residuals
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B-Diagnostic Plots of  Residuals Predicted Values Residuals Suggests quadratic specification
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Models with Quadratics Econ 321-Stéphanie Lluis 11 Turning point x*=0.298/[2*(0.0061)]=24.4
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12 Econ 321-Stéphanie Lluis
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Models with Log Log(price) =  β 0  +  β 1 log(nox)  +  β 2 bdrooms β elasticity of price with respect to pollution β change in logprice for  Δ bdrooms=1 Δ log(price)=  β 2 Δ bdrooms
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