The attached student project is a good illustration of selecting explanatory variables for a regression model. The candidates focuses on the multicollinearity among the three explanatory variables, and he uses F tests to exclude one of the variables.

Linear regression is linear in the parameters. Transformations of the explanatory variables, such as taking logarithms or square roots, may improve the fit. Similarly, generalized linear models for class ratemaking may fit the explanatory variables to the logarithm of the dependent variable, converting additive equations into an multiplicative model.

Outliers may distort an actuarial analysis. A claim severity figure may have a typo that multiplies the figure by ten. As the textbook says, comparing the fitted regression line with a line formed by omitting an outlier is especially important for small data sets.

Similar student projects can be done for wine tasting and other characteristics of quality. The determinants of wine taste are disputed: age, vinery, weather conditions, soil attributes, and a host of other factors are thought to influence wines.

Many web sites on wines have data that you might use for a student project; use Google or another search engine to find good data. Develop hypotheses about the determinants of wine taste, and use the statistical techniques in the on-line course to test the hypotheses.