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.