Budgeting Basics and Beyond

16.3. Regression Statistics

Regression analysis is a statistical method. Therefore, it uses a variety of statistics to tell about the accuracy and reliability of the regression results. They include:

• Correlation coefficient (r) and coefficient of determination (R²)

• Standard error of the estimate (S_e) and prediction confidence interval

• Standard error of the regression coefficient (S_b) and t-statistic

Each of these statistics is explained next.

Correlation Coefficient (r) and Coefficient of Determination (R²)

The correlation coefficient r measures the degree of correlation between Y and X. The range of values it takes on is between −1 and +1. More widely used, however, is the coefficient of determination, designated R². Simply put, R² tells us how good the estimated regression equation is. In other words, it is a measure of "goodness of fit" in the regression. Therefore, the higher the R², the more confidence we have in our estimated equation.

More specifically, the coefficient of determination represents the proportion of the total variation in Y that is explained by the regression equation. It has the range of values between 0 and 1.

Example 3

The statement " Sales is a function of advertising expenditure with R² = 70 percent" can be interpreted as "70 percent of the total variation of sales is explained by the regression equation or the change in advertising, and the remaining 30 percent is accounted for by something other than advertising, such as price and income."

The coefficient ...