- Exercise #9, p. 227
- Project 4.5, p. 230
- replace section 5.3 with two days of work on projects (just
prior to project presentations on the 25th of April - it's coming up!).
- Optional Project:
You have two "Project" grades so far. If you would like to replace one of them with another (because of a poor grade, for example), you may choose one of the following projects:
- 4.7
- 4.8
- 4.13 (using this data set)
- or you may propose another
- Example: Russ's Project (test evaluations) - simple linear regression
- Scatter plot and simple regression line (obvious linear
correlation!):
- Output:
Linear Regression: Estimate SE Prob Constant 2.11374 (5.486696E-2) 0.00000 Variable 0 0.524759 (1.309028E-2) 0.00000 R Squared: 0.467971 Sigma hat: 0.297018 Number of cases: 1829 Degrees of freedom: 1827 Source df SS MS F ratio Regression 1 141.77142 141.77142 1607.0250 Residual 1827 161.17757 8.82197954E-2 Prob(f)=0.0000 Lack of Fit 219 23.026099 .10514200 1.2237897 Pure Error 1608 138.15147 8.59150918E-2 Prob(f)=0.2688
- Residuals: do they appear normal?
- Additional "Russ plots"
- Scatter plot and simple regression line (obvious linear
correlation!):
- Multiple Regression
We'll look over the example from the section, then try it with Russ's data.
- The big picture: so-called step-wise regression: add variables/Subtract variables until the best model for fewest number of variables is found.
- Use t-tests to get significance of individual predictors.
- Unfortunately, the procedure is not transitive: even though predictor u may not be significant in model (u,v,w), it may be the best single regression variable!
- Curvilinear regression
- Basis function are non-linear in x
- but linear in parameters - that's what's important!
- The usual regression diagnostics apply.