CHAPTER 2 ECONOMETRICS x x x x x THE MEANING OF REGRESSION Dependent variable explained by Independent variables Price of iTune Consumer income Price of.

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CHAPTER 2 ECONOMETRICS x x x x x THE MEANING OF REGRESSION Dependent variable explained by Independent variables Price of iTune Consumer income Price of CD Quantity of iTunes demanded

Price ($) Quantity (100s) Price of iTune Consumer income Price of CD Quantity of iTunes demanded Y X1X1 X2X2 X3X3 Y = b 1 + b 2 X

Price ($) Quantity (100s) XiXi YiYi E(Y i )eiei Y i = b 1 + b 2 X i + e i E(Y) = b 1 + b 2 X E(Y) = X

ABC Random Number Generation Number of variables No. of Random No. Distribution Mean = Random Seed: Output range: OK Cancel Help Stnd deviation = 0 $A$1:$A$8 1 Tools Data analysis

fx CtrlShiftEnter

Cumulative fx Function Arguments X Formula result = OKCancel NORMDIST Mean Stnd_dev Cumulative A TRUE Cum Norm

Population Regression Function (PRF) the way the world works but we can’t observe this directly Sample Regression Function (SRF) an estimate of the PRF based on a sample ordinary least squares (OLS) is method used Y i = B 1 + B 2 X i + u i Y i = b 1 + b 2 X i + e i

Ordinary Least Squares (OLS) OLS minimizes: The residual sum of squares (RSS) E(Y i ) = Y i = b 1 + b 2 X i e i = Y i – Y i ∑ e i 2 = ∑ (Y i – Y i ) 2

b 1 = Y - b 2 X b 2 = ∑ (X i – X)(Y i – Y) ∑ (X i – X) 2 Y =Y = ∑ Y i n

Price ($) Quantity (100s) b 2 = ∑ (X i – X)(Y i – Y) ∑ (X i – X) 2 b 1 = Y - b 2 X

XiXi YiYi E(Y i ) eiei ei2ei ,025 4, ,545 ∑ei2∑ei2

VAR0001VAR0002var Linear Regression Dependent VAR0001 Method: Statistics Plots Save Options Independent(s) PreviousNext Enter ▼ OKResetCancelHelp VAR0002 AnalyzeRegressionLinear

Unstandardized Coeffic Stndardzd Coeffic BBetaStd. Error Model 1 (Constant) X tSig. XiXi eiei E(Y) = 550 − 250 X The residuals are uncorrelated with the independent variable.

ABC fx Function Arguments Array1 Formula result = OKCancel CORREL Array2 A1:A5 B1:B5

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