Use the value of the correlation coefficient r to calculate...

Use the value of the correlation coefficient $r$ to calculate the coefficient of determination $r^{2}$. What does this tell you about the explained variation of the data about the regression line? About the unexplained variation?
$$r=-0.957$$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Explained Variation

Explained variation refers to the part of the total variance in the data that is captured by the regression model. Here, about 91.5% of the data’s variance is explained, indicating that the model fits the data well in this regard.

Unexplained Variation

Unexplained variation is the portion of the total variance that is not accounted for by the regression model, typically due to factors not included in the model or inherent randomness. In this case, since 91.5% is explained, approximately 8.5% remains unexplained.

Correlation Coefficient

The correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. Its values lie between -1 and 1, where values closer to -1 or 1 indicate strong relationships. In this context, an r value of -0.957 indicates a strong negative linear relationship.

Coefficient of Determination

The coefficient of determination (r²) is obtained by squaring the correlation coefficient, offering a measure of the proportion of variance in the dependent variable that is explained by the independent variable. With r = -0.957, r² is approximately 0.915, meaning the regression model accounts for about 91.5% of the variance in the data.

Transcript

Please give Ace some feedback