November 2008
Beginner
448 pages
11h 33m
English
Content preview from Budgeting Basics and Beyond
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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 (Se) and prediction confidence interval
Standard error of the regression coefficient (Sb) 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 ...
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