Question

The owner of a new pizzeria in town wants to study the relationship between weekly revenue and advertising expenditures. All measures are recorded in thousands of dollars. The summary output for the regression model is given below.

ANOVA
dfdf SSSS MSMS FF Significance FF
Regression 8 19.7514782 2.46893478 20.63809579 9.1073E-09
Residual 23 2.751489304 0.11962997
Total 31 22.50296750

What is the coefficient of determination for this model, R2?

Answer 1

The coefficient of determination, R-squared (R²), measures the proportion of the variation in the dependent variable that can be explained by the independent variable using the regression model. In this case, R² is approximately 44%, indicating that 44% of the variation in the weekly revenue can be explained by the variation in the advertising expenditures.

Step-by-step explanation:

The coefficient of determination, also known as R-squared (R²), measures the proportion of the variation in the dependent variable (weekly revenue) that can be explained by the independent variable (advertising expenditures). It represents the percentage of variation in the weekly revenue that is accounted for by the variation in the advertising expenditures using the regression model.

In this case, the coefficient of determination, R², is 0.4397 or approximately 44%. This means that approximately 44% of the variation in the weekly revenue can be explained by the variation in the advertising expenditures, while the remaining 56% is due to other factors not included in the model.