UCLA ECON 103 - Econ-103-Lecture-05 (74 pages)

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Econ-103-Lecture-05



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Econ-103-Lecture-05

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Pages:
74
School:
University of California, Los Angeles
Course:
Econ 103 - Introduction to Econometrics
Introduction to Econometrics Documents

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Lecture Note 5 Prediction Goodness of Fit and Modelling Issues Moshe Buchinsky UCLA Fall 2014 Buchinsky UCLA Ec 103 Lecture 5 Fall 2014 1 74 Topics to be Covered 1 Least Square Prediction 2 Measuring Goodness of t 3 Modeling Issues 4 Polynomial Models 5 Log linear Models 6 Log log Models Buchinsky UCLA Ec 103 Lecture 5 Fall 2014 2 74 Least Squares Predictions Least Squares Predictions The ability to predict is important to Business economists and nancial analysts who attempt to forecast the sales and revenues of speci c rms Government policy makers who attempt to predict the rates of growth in national income in ation investment saving social insurance program expenditures etc Buchinsky UCLA Ec 103 Lecture 5 Fall 2014 3 74 Least Squares Predictions Accurate predictions provide a basis for better decision making in every type of planning context In order to use regression analysis as a basis for prediction we must assume that y0 and x0 are related to one another by the same regression model that describes our sample of data In particular assumption SR1 holds for these observations namely y0 1 2 x0 e0 4 1 where e0 is a random error Buchinsky UCLA Ec 103 Lecture 5 Fall 2014 4 74 Least Squares Predictions The task of predicting y0 is related to the problem of estimating E y0 1 2 x0 Although E y0 1 2 x0 is not random the outcome y0 is random The least squares predictor of y0 comes from the tted regression line yb0 b1 b2 x0 Buchinsky UCLA Ec 103 Lecture 5 4 2 Fall 2014 5 74 Least Squares Predictions Figure 4 1 A point prediction Buchinsky UCLA Ec 103 Lecture 5 Fall 2014 6 74 Least Squares Predictions To evaluate how well this predictor performs we de ne the forecast error which is analogous to the least squares residual f y0 yb0 1 2 x0 e0 b1 b2 x 0 4 3 We would like the forecast error to be small Taking the expected value of f we nd that E f 1 2 x 0 E e0 1 2 x0 0 0 E b1 E b2 x0 1 2 x0 This means that on average the forecast error is zero or yb0 is an unbiased predictor of



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