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Coefficient Determination 5A2D94

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Coefficient Determination 5A2D94


1. **Problem statement:** We are given the sum of squares due to regression (SSR) and the total sum of squares (SST) from a wine quality model. We need to find the coefficient of determination, $r^2$, and interpret its meaning. 2. **Formula:** The coefficient of determination $r^2$ is calculated as: $$r^2 = \frac{SSR}{SST}$$ where SSR is the sum of squares due to regression and SST is the total sum of squares. 3. **Given values:** $$SSR = 18573$$ $$SST = 28146$$ 4. **Calculation:** $$r^2 = \frac{18573}{28146} \approx 0.6597$$ Rounded to three decimal places: $$r^2 \approx 0.660$$ 5. **Interpretation:** The coefficient of determination $r^2 = 0.660$ means that approximately 66.0% of the variability in wine quality can be explained by the alcohol content in the model. This indicates a moderately strong relationship between alcohol content and wine quality in this sample.