Question

for a particular regression analysis, sst = 184.8594 and ssr = 159.0879.
a. obtain the coefficient of determination.
b. determine sse.

a. determine the value of $r^2$, the coefficient of determination.
$r^2 = \square$
(round to four decimal places as needed.)

Explanation:

Step1: Recall formula for \( r^2 \)

The coefficient of determination \( r^2 \) is given by the formula \( r^2=\frac{SSR}{SST} \), where \( SSR \) is the sum of squares due to regression and \( SST \) is the total sum of squares.
We know that \( SST = 184.8594 \) and \( SSR = 159.0870 \).

Step2: Calculate \( r^2 \)

Substitute the given values into the formula:
\( r^2=\frac{159.0870}{184.8594} \)
Calculate the division: \( \frac{159.0870}{184.8594}\approx0.8606 \) (rounded to four decimal places).

Answer:

\( r^2\approx\boxed{0.8606} \)