1. Economics 310 Lecture 6 Test for a Regression

2. Basic Hypothesis

3. Developing Test

4. F-Distribution

5. Logic of Test F f(F) 0 Non-Rejection Region Rejection Region  FcFc HAHA H0H0

6. Cigarette Demand Example VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 24 DF P-VALUE CORR. COEFFICIENT AT MEANS Y 0.11255E-03 0.6637E-04 1.696 0.103 0.327 0.4512 0.2116 P -0.16941 0.9552E-01 -1.774 0.089-0.340 -0.3751 -0.1586 QLAG 0.65779 0.1505 4.370 0.000 0.666 0.6803 0.6554 CONSTANT 0.64609 0.2588 2.497 0.020 0.454 0.0000 0.2916 VARIANCE-COVARIANCE MATRIX OF COEFFICIENTS Y 0.44050E-08 P -0.55953E-05 0.91240E-02 QLAG -0.76874E-05 0.85602E-02 0.22658E-01 CONSTANT 0.10231E-04 -0.14519E-01 -0.35764E-01 0.66967E-01 Y P QLAG CONSTANT

7. Calculating the F

8. Simplifying the Calculation

9. Anova Table ANALYSIS OF VARIANCE - FROM MEAN SS DF MS F REGRESSION 1.2016 3. 0.40055 28.565 ERROR 0.33653 24. 0.14022E-01 P-VALUE TOTAL 1.5382 27. 0.56969E-01 0.000

10. F and R 2

11. Calculating F via R 2 - Example