1. Statistics 400 - Lecture 22

2. zLast Day: Regression zToday: More Regression

3. Example (radiation): zTest the hypothesis that the intercept is 0 with significance level 0.05 z95% Confidence Interval

4. Estimation of the Mean Response at a Specified x zWhy would we want to compute the regression line? zEstimated mean response at a specified x zPrediction of a future response at a specified x z What is the difference?

5. CI for the Mean Response at a Specified x zA confidence interval for the mean response is:

6. Prediction Interval for a Single Response at a Specified x zA prediction interval for a future response is:

7. Example (radiation): zGive a 95% confidence interval for the mean response when the radiation is 24 picocuries/L zGive a 95% prediction interval for the a single response when the radiation is 24 picocuries/L

8. Example (radiation): zGive a 95% confidence interval for the mean response when the radiation is 24 picocuries/L zGive a 95% prediction interval for the a single response when the radiation is 24 picocuries/L

9. Checking Model Assumptions zWhat assumptions have we made about the linear regression model? zHow can we check these?

10. Checking Normality zCan view residuals as estimates of the errors, e i zWhat is the distribution of e i ’s ? zHow can we assess the validity of this assumption?

11. Checking Constant Error Variance zThe errors should be independent and identically distributed zIf the residuals are plotted versus the predicted responses, we should see

12. Checking Independence zThe error in one observation should not effect the error in other observations zHow might we plot the residuals to check this assumption?

13. Example (cont.) zData: The table below gives the average radioactivity in milk samples and the percent increase in the number of deaths for 9 regions of the U.S.A. zRecall,

18. Computer Output zWill not normally compute regression line, standard errors, … by hand zKey will be identifying what computer is giving you

19. SPSS Example

20. zWhat is the Model Summary? zWhat is the ANOVA Table

21. zWhat is the Coefficients Table?