1 / 14

No Intercept Regression and Analysis of Variance

No Intercept Regression and Analysis of Variance. Example Data Set. Estimate two models. Model with y-intercept Y = a + b * X. Model no y-intercept Y = b * X. Observations. The model with a y-intercept is more complex than the model with no y-intercept.

heather
Download Presentation

No Intercept Regression and Analysis of Variance

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. No Intercept Regression and Analysis of Variance

  2. Example Data Set

  3. Estimate two models • Model with y-interceptY = a + b * X • Model no y-interceptY = b * X

  4. Observations • The model with a y-intercept is more complex than the model with no y-intercept. • One would expect then that the R2 of the model would decline when the y-intercept is removed. BUT, the R2 actually increases. • If the explanatory power of the model, R2, increases, then the error of the model, Standard Error, should decrease. But, the Standard Error actually increases.

  5. Analysis of Variance Tablemodel with y-intercept

  6. Analysis of Variance Tablemodel no y-intercept

  7. Comparison of Sum of Squares

  8. Revision of Sum of Squaresfor no-intercept model This is re-calculated. These are from the model with a y-intercept.

  9. Comparison of Revised Sum of Squares

  10. Revised Statistics • Model no y-interceptY = b * X SSR / SST = 24.53 / 25.64 = 0.957 √ SSE / d.o.f. = √1.11 / 9 = 0.351

  11. Comparison of Revised Statistics • Model with y-interceptY = a + b * X • Model no y-interceptY = b * X

  12. Revised Observations • The model with a y-intercept is more complex than the model with no y-intercept. • One would expect then that the R2 of the model would decline when the y-intercept is removed. BUT, the R2 actually increases. • If the explanatory power of the model, R2, increases, then the error of the model, Standard Error, should decrease. But, the Standard Error actually increases. R2 decreases and the Standard Error increases. Explanatory power declines and error increases

  13. Analysis of Variance Tablemodel no y-interceptREVISED SS / df FDIST (199.43, 1,9) MSR/ MSE

  14. Summary • When comparing a model with a y-intercept to the same model without a y-intercept • Revise the ANOVA table for the no-intercept model with values from the y-intercept model (X). • Recalculate necessary items (Y), and the R2 and the Standard Error.

More Related