Analysis of Financial Data

Chapter 6. Multiple regression

The discussion of simple regression in Chapter 5 involved two variables: the dependent variable, Y, and the explanatory variable, X. As we discussed at the beginning of Chapter 4, many analyses in business and finance involve many variables. Multiple regression extends simple regression to the case where there are many explanatory variables. Fortunately, most of the intuition and statistical techniques of multiple regression are very similar to those of simple regression.

The key elements of Chapters 4 and 5 were:

1. The development of graphical intuition for regression techniques as the fitting of a straight line through an XY-plot.

2. The introduction of the regression coefficient as measuring a marginal effect.

3. The description of the OLS estimate as a best fitting line (in terms of minimizing the sum of squared residuals) through an XY-plot.

4. The introduction of R² as a measure of fit of a regression model.

5. The introduction of statistical techniques such as confidence intervals and hypothesis tests.

With some exceptions (highlighted below) these five elements do not differ for the multiple regression model. You should look back on Chapters 4 and 5 if you are having difficulty remembering the underlying intuition or statistical aspects of regression. This chapter covers these five elements for the multiple regression case very briefly, summarizing similarities with and differences from the simple regression model. Much of the chapter will involve the discussion ...