In a regression analysis with r² = 0.72 for profits and advertising spending, what can be concluded?

In a regression analysis with r² = 0.72 for profits and advertising spending, what can be concluded?

• A. 72% of the variability is explained
• B. There is no correlation
• C. The linear model is inappropriate
• D. The slope is negative

Answer: (A)

When r² = 0.72, it indicates that 72% of the variability in the dependent variable, which in this case is profits, can be explained by the independent variable, advertising spending. This means that a significant portion of the variation in profits can be accounted for by changes in advertising spending, suggesting a strong relationship between the two variables within the context provided. This metric serves as a gauge of the explanatory power of the regression model, confirming that a substantial amount of the data variability is captured by the model. In essence, the high r² value suggests that the regression model is effective in explaining the relationship between advertising expenditures and profits.

When r² = 0.72, it indicates that 72% of the variability in the dependent variable, which in this case is profits, can be explained by the independent variable, advertising spending. This means that a significant portion of the variation in profits can be accounted for by changes in advertising spending, suggesting a strong relationship between the two variables within the context provided.

This metric serves as a gauge of the explanatory power of the regression model, confirming that a substantial amount of the data variability is captured by the model. In essence, the high r² value suggests that the regression model is effective in explaining the relationship between advertising expenditures and profits.