1 / 18

Chapter 4

Chapter 4. Using Regression to Estimate Trends. Trend Models. Linear trend, Quadratic trend Cubic trend Exponential trend. Choosing a trend. Plot the data, choose possible models Use goodness of fit measures to evaluate models Try to Minimize the AIC and SBC Choose a model.

victor-turner
Download Presentation

Chapter 4

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 4 Using Regression to Estimate Trends

  2. Trend Models • Linear trend, • Quadratic trend • Cubic trend • Exponential trend

  3. Choosing a trend • Plot the data, choose possible models • Use goodness of fit measures to evaluate models • Try to Minimize the AIC and SBC • Choose a model

  4. Mean Squared Error

  5. Goodness of Fit Measures • Coefficient of Determination or R2

  6. Goodness of Fit Measures • Adjusted R2

  7. AIC and SBC

  8. AIC and SBC(continued) • Choose the model that minimizes the AIC and SIC • Examples • choose AIC=3 over AIC=7 • choose SIC=-7 over SIC=-5 • The SIC has a larger penalty for extra parameters!

  9. F-Test The F-test tests the hypothesis that the coefficients of all explanatory variables are zero. A p-value less than .05 rejects the null and concludes that our model has some value.

  10. Testing the slopes • T-test tests a hypothesis about a coefficient. • A common hypothesis of interest is:

  11. Steps in a T-test • 1. Specify the null hypothesis • 2. Find the rejection region • 3. Calculate the statistic • 4. If the test statistic is in the rejection region then reject!

  12. Figure 5.1 Student-t Distribution f(t) () /2 /2 0 tc t -tc red area = rejection region for 2-sided test

  13. An Example,n=264 f(t) .95 .025 .025 0 t -1.96 1.96 red area = rejection region for 2-sided test

  14. LS // Dependent Variable is CARSALES Date: 02/17/98 Time: 13:44 Sample: 1976:01 1997:12 Included observations: 264 Variable Coefficient Std. Error t-Statistic Prob. C 13.10517 0.311923 42.01413 0.0000 TIME 0.000882 0.005479 0.160947 0.8723 TIME2 2.52E-05 2.02E-05 1.248790 0.2129 R-squared 0.107295 Mean dependent var 13.80292 Adjusted R-squared 0.100454 S.D. dependent var 1.794726 S.E. of regression 1.702197 Akaike info criterion 1.075139 Sum squared resid 756.2412 Schwarz criterion 1.115774 Log likelihood -513.5181 F-statistic 15.68487 Durbin-Watson stat 0.370403 Prob(F-statistic) 0.000000

  15. Using our results Plugging in our estimates: Not in the rejection region, don’t reject!

  16. P-Value=lined area=.8725 f(t) .95 .025 .025 0 t -1.96 1.96 .016 red area = rejection region for 2-sided test

  17. Ideas for model building • F-stat is large, p-value=.000000 implies our model does explain something • “Fail to reject” does not imply accept in a t-test • Idea, drop one of the variables

  18. LS // Dependent Variable is CARSALES Date: 02/17/98 Time: 14:00 Sample: 1976:01 1997:12 Included observations: 264 Variable Coefficient Std. Error t-Statistic Prob. C 12.81594 0.209155 61.27481 0.0000 TIME 0.007506 0.001376 5.454057 0.0000 R-squared 0.101961 Mean dependent var 13.80292 Adjusted R-squared 0.098533 S.D. dependent var 1.794726 S.E. of regression 1.704014 Akaike info criterion 1.073520 Sum squared resid 760.7597 Schwarz criterion 1.100611 Log likelihood -514.3044 F-statistic 29.74674 Durbin-Watson stat 0.368210 Prob(F-statistic) 0.000000

More Related