Lecture 3

1. Lecture 3 HSPM J716

2. New spreadsheet layout • Coefficient • Standard error • T-statistic • Coefficient ÷ its Standard error

3. Standard error of coefficient • Shows how near the estimated coefficient might be to the true coefficient.

4. Confidence interval for a coefficient • Coefficient ± its standard error × t from table • 95% probability that the true coefficient is in the 95% confidence interval? • If you do a lot of studies, you can expect that, for 95% of them, the true coefficient will be in the 95% confidence interval.

5. Standard error of the regression • Should be called standard residual • But it isn’t

6. Assumptions • Required for using linear least squares model • Illustrated in assignment 2

7. Durbin-Watson statistic • Serial correlation • For clinic 2

8. Confidence interval for prediction • The hyperbolic outline

9. Formal outlier test? • Using confidence interval of prediction

10. Multiple regression • 3 or more dimensions • 2 or more X variables • Y = α + βX + γZ + error • Y = α + β1X1 + β2X2 + … + βpXp error

11. Fitting a plane in 3D space • Linear assumption • Now a flat plane • The effect of a change in X1 on Y is the same at all levels of X1 and X2 and any other X variables. • Residuals are vertical distances from the plane to the data points floating in space.

12. β interpretation • in Y = α + βX + γZ + error • β is the effect on Y of changing X by 1, holding Z constant. • Often, there is a linear relationship between X and Z. When X is one unit bigger than you would predict it to be, based on what Z is, then we expect Y to be β more than you would expect from what Z is.

13. β-hat formula • in Y = α + βX + γZ + error • See pdf file

14. LS • Spreadsheet as front end • Word processor as back end • Interpretation of results • Coefficients • Standard errors • T-statistics • P-values • Prediction