1. 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

2. .2.4.6.811.2 1 2 3 4 5 6 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

3. .2.4.6.811.2 1 2 3 4 5 6 Price ($) Quantity (100s) XiXi 0.2 0.4 0.6 1.0 YiYi E(Y i )eiei Y i = b 1 + b 2 X i + e i E(Y) = b 1 + b 2 X E(Y) = 550 - 250 X

4. ABC 1 2 3 4 5 6 7 8 9 10 11 -0.23002 0.389811 0.211674 1.31909 0.785948 0.017634 -1.3149 -1.32496 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

5. 49 50 51 52 53 54 55 56 57 58 59 -1.3149 -1.32496 -3 -2 0 1 2 3 fx 0 4 7 13 19 7 0 CtrlShiftEnter 0 4 7 13 19 7 0 -2-1012

6. 52 53 54 55 56 57 58 59 -3 -2 0 1 2 3 0 4 7 13 19 7 0 Cumulative fx Function Arguments X Formula result = OKCancel NORMDIST Mean Stnd_dev Cumulative 0.001 0.023 0.159 0.500 0.841 0.977 0.999 A53 0 1 TRUE Cum Norm

7. 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

8. 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

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

10. .2.4.6.811.2 1 2 3 4 5 6 Price ($) Quantity (100s) b 2 = ∑ (X i – X)(Y i – Y) ∑ (X i – X) 2 b 1 = Y - b 2 X

11. XiXi 0.2 0.4 0.6 1.0 YiYi 490 505 336 318 E(Y i ) 500 450 400 300 eiei -10 55 -64 18 ei2ei2 100 3,025 4,096 324 7,545 ∑ei2∑ei2

12. VAR0001VAR0002var 1 2 3 4 5 6 0.2490 0.4505 0.6336 1.0318 1.2249 Linear Regression Dependent VAR0001 Method: Statistics Plots Save Options Independent(s) PreviousNext Enter ▼ OKResetCancelHelp VAR0002 AnalyzeRegressionLinear

13. Unstandardized Coeffic Stndardzd Coeffic BBetaStd. Error 549.837 -250.349 46.833 60.461-.923 Model 1 (Constant) X1 11.740 -4.141.001.026 tSig. XiXi 0.2 0.4 0.6 1.0 eiei -10 55 -64 18 1.2 E(Y) = 550 − 250 X The residuals are uncorrelated with the independent variable.

14. ABC 1 2 3 4 5 6 7 0.2-10 0.455 0.6-64 1.018 1.2 fx Function Arguments Array1 Formula result = OKCancel CORREL Array2 A1:A5 B1:B5