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Unformatted text preview: MULTIPLE REGRESSION
Read (Chapters 6 and 7) Has two or more regressors (independent Has variables) variables) May solve the omitted variable bias May problem problem SPECIFICATION ERROR
(1) Omission of relevant independent (1) variables (Hence omitted variable bias) variables (2) Inclusion of Irrelevant independent Inclusion variables variables (3) Wrong functional form OMITTED VARIABLE BIAS: TWO CONDITIONS
Omitted variable must affect the dependent Omitted variable variable Omitted variable must be correlated with Omitted the included independent variable the OMITTED VARIABLES: EFFECTS (1) OLS estimator biased in general. This bias is (1) called specification error bias or omitted variable bias. bias. OLS standard errors unreliable. Specifically, the OLS OLS standard errors will be smaller than what they should be, in which case the t-ratios are bigger (hence, more likely to reject the null hypothesis of no significance)-unless the correlation coefficient between omitted independent variable and included independent variable is zero. variable OMITTED VARIABLE BIAS: SOLUTIONS
(1)Add omitted variable(s) to regression (2)Divide data into groups MULTIPLE REGRESSION: SPECIFICATION MULTIPLE REGRESSION: INTERPRETATION OF COEFFICIENTS MULTIPLE REGRESSION: ASSUMPTIONS MULTIPLE REGRESSION: THE METHOD OF OLS MULTIPLE REGRESSION: PREDICTED VALUES MULTIPLE REGRESSION: RESIDUALS MULTIPLE REGRESSION: SER MULTIPLE REGRESSION: ANOVA TABLE GOODNESS-OF-FIT: RSQUARED GOODNESS-OF-FIT: ADJUSTED R-SQUARED R-SQUARED & ADJUSTED RSQUARED TELL YOU WHETHER Predictive ability of regressors is good i.e. Predictive higher values indicate better predictability higher R-SQUARED AND ADJUSTED RSQUARED DO NOT TELL YOU WHETHER
(1)An included variable is statistically (1)An significant significant (2)The regressors are a true cause of the (2)The movements in the dependent variable movements (3)There is omitted variable bias (4)You have chosen the most appropriate (4)You set of regressors set CONFIDENCE INTERVALS MULTIPLE REGRESSION: HYPOTHESIS TESTING MULTIPLE REGRESSION: HYPOTHESIS TESTING Contd. MULTIPLE REGRESSION: HYPOTHESIS TESTING Contd. MULTIPLE REGRESSION: HYPOTHESIS TESTING Contd. MULTIPLE REGRESSION: HYPOTHESIS TESTING Contd. MULTIPLE REGRESSION: HYPOTHESIS TESTING Contd. EXAMPLE EXAMPLE: Contd. EXAMPLE: Contd EXAMPLE: Contd EXAMPLE: Contd. EXAMPLE: Contd. EXAMPLE: Contd. EXAMPLE: Contd. EXAMPLE: Contd EXAMPLE: Contd. EXAMPLE: SUMMARY ...
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This note was uploaded on 04/28/2011 for the course ECON 2P91 taught by Professor Ogwang during the Winter '09 term at Brock University.
- Winter '09