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Lecture_4_Regression_Part_2

# Lecture_4_Regression_Part_2 - 1 Lecture 4(Part 2 Regression...

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Lecture 4 (Part 2) Regression and Forecasting Read: (WK Ch 4, 5; other books) EC 413/513 Economic Forecast and Analysis (Professor Lee) 1

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Topics: Regression for Forecasting Trend and Seasonality Regression for Demand Analysis More on Regression Analysis Practical Application (mini project) 1. Overview of Regression Analysis Three goals of Regression Analysis Prediction (Forecasting ) Marginal Effects (coefficients) Testing Hypothesis (significance of coefficients) Example) Hedonic Pricing Models [Econometric model] Price = α + β 1 SQFT + β 2 YEAR + β 3 POOL + e Parameters (coefficients): α , β 1 , β 2 , β 3 Error term: e imaginary term (Do not omit this term, however) 2
[Estimation Results] (A) Simple Regression Predicted_Price = 52,404 + 61.16 SQFT (i) Prediction If SQFT = 2,850 , Predicted_Price = 52,404 + 61.16 * 2850 = \$226,708 (ii) Marginal effect of SQFT = \$61.16 Price / SQFT = 61.16 “One more unit of SQFT (1 square foot) will lead to \$61.16 increase in price.” (iii) Testing Hypothesis (on the coefficients : parameters ) H 0 : β 1 = 0 H a : β 1 0 “Significance of the coefficient of SQFT or, specifically, H 0 : β 1 = 100 H a : β 1 100 3

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(B) Multiple Regression Predicted_Price = -7,434,369 + 63.38 SQFT + 3,753 YEAR (i) Prediction If SQFT = 2,850, YEAR = 1991, then Predicted_Price = -7,434,369 + 63.38 * 2850 + 3,753 * 1991 = \$219,171.60 (ii) Marginal effect of SQFT = 63.38 Price / SQFT = 63.38 (partial effect after controlling the effect of YEAR ) “One more unit of SQFT will lead to \$63.38 increase in price.” (iii) Testing Hypothesis H 0 : β 1 = 0 H a : β 1 0 “Significance of the coefficient ( β 1 ) of SQFT or on the coefficient of YEAR ( β 2 )” On the other hand, one may consider H 0 : β 1 = 0, β 2 = 0 H a : H 0 is not true “Joint Significance of the coefficients of SQFT and YEAR” (F-test) 4
General Notation : Population regression Model y = α + β X + u (Price = α + β SQFT + u) or y i = α + β X i + u i (Price i = α + β SQFT i + u i ) where u i = error term Sample regression Model y i = + X i + i where i = residual or i = + X i y i = i + i Estimation: Find and such that SSR (Sum of squared residuals) is at the minimum. In the simple regression, y i = + X i + i = = - 5

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[Handout] Algebra of Simple Regression and t-statistic Simple Regression : y t = + X t + t Data X t y t (X t - ) (y t - ) (X t - ) *(y t - ) (X t - ) 2 = + X t t = y t - t 2 1 3 2 5 3 4 Coefficient estimates = , = - (X t - )( y t - ) = (X t - ) 2 = = = Thus, = + X t = t-statistic t* = SE() = s 2 = t 2 SSR = 2 = s 2 = SE() = Thus, t* = 6
Exercise X t y t (X t - ) (y t - ) (X t - ) *(y t - ) (X t - ) 2 = + X t t = y t - t 2 1 4 2 3 3 5 Find , and t*. Two Important Issues:

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Lecture_4_Regression_Part_2 - 1 Lecture 4(Part 2 Regression...

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