Question

Based on the below data what will be the value of multiple R?
SSR=27, SSE=28

Answer 1

To calculate the multiple R (the multiple correlation coefficient), we can use the formula:

\[
R = \sqrt{R^2}
\]

where \( R^2 \) (the coefficient of determination) can be calculated using:

\[
R^2 = \frac{SSR}{SST}
\]

In this context:

- SSR (Sum of Squares for Regression) = 27
- SSE (Sum of Squares for Error) = 28
- SST (Total Sum of Squares) is the sum of SSR and SSE:

\[
SST = SSR + SSE = 27 + 28 = 55
\]

Now we can calculate \( R^2 \):

\[
R^2 = \frac{SSR}{SST} = \frac{27}{55}
\]

Next, we need to calculate \( R \):

\[
R = \sqrt{R^2} = \sqrt{\frac{27}{55}}
\]

Calculating this value gives:

\[
R \approx \sqrt{0.4909} \approx 0.701
\]

Thus, the value of multiple R is approximately **0.701**.