What would be the coefficient of determination if the total sum of squares (SST) is 23.29 and the sum of squares due to regression (SSR) is 10.03?

1. Break Down the Problem

To find the coefficient of determination ($R^2$), we need to use the following formula: $R^2 = \frac{SSR}{SST}$ Where:

• $SSR$ is the sum of squares due to regression.
• $SST$ is the total sum of squares.

2. Relevant Concepts

Understanding the formula is critical:

• The coefficient of determination $R^2$ indicates the proportion of variance in the dependent variable that is predictable from the independent variable(s).

3. Analysis and Detail

1. Given:

   • $SST = 23.29$
   • $SSR = 10.03$

2. Substitute the values into the formula: $R^2 = \frac{10.03}{23.29}$

4. Verify and Summarize

Now we perform the calculation: $R^2 = \frac{10.03}{23.29} \approx 0.430$ This indicates that approximately 43% of the variability in the dependent variable can be explained by the independent variable(s).

Final Answer

The coefficient of determination $R^2$ is approximately 0.430.