Question 1200525: Use the value of the linear correlation coefficient to calculate the coefficient of determination. What does this tell you about the explained variation of the data about the regression line? About the unexplained variation?
r=0.445
Answer by GingerAle(43)   (Show Source):
You can put this solution on YOUR website! The coefficient of determination (R²) is calculated as the square of the correlation coefficient (r):
R² = r² = 0.445² = 0.1980
**Interpretation:**
* **Explained Variation:** The coefficient of determination (R²) of 0.1980 indicates that approximately 19.80% of the variation in the dependent variable (the variable being predicted) can be explained by the linear relationship with the independent variable. In other words, 19.80% of the variability in the data can be accounted for by the regression line.
* **Unexplained Variation:** The remaining 1 - R² = 1 - 0.1980 = 0.8020, or 80.20%, of the variation in the dependent variable cannot be explained by the linear relationship with the independent variable. This unexplained variation may be due to other factors not considered in the model, random error, or the limitations of the linear model itself.
**In summary:**
The R² value of 0.1980 suggests that the linear regression model explains a relatively small proportion of the variation in the data. This implies that the model may not be very effective in predicting the dependent variable based on the independent variable.
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