# Here is partial output from a simple regression analysis. The regr

Here is partial output from a simple regression analysis.
The regression equation is
EAFE = 4.76 + 0.663 S&P
Analysis of Variance
$\begin{array}{cc} Source & DF & SS & MS & F & P \\ Regression & 1 & 3445.9 & 3445.9 & 9.50 & 0.005 \\ Residual \ Error & & & & & \\ Total & 29 & 13598.3 & & & \\ \end{array}$
Calculate the values of the following:
The regression standard error, $$\displaystyle{s}_{{{e}}}$$ (Round to 3 decimal places)
The coefficient of determination, $$\displaystyle{r}^{{{2}}}$$ (Round to 4 decimal places)
The correlation coefficient, r (Round to 4 decimal places)

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Step 1
The formula of $$\displaystyle{S}_{{{e}}}$$ is as follows:
$$\displaystyle{S}_{{{e}}}=\sqrt{{{\frac{{{S}{S}{T}-{S}{S}{R}}}{{{d}{f}_{{{\left(to{t}{a}{l}\right)}}}-{d}{f}_{{{\left({s}{o}{u}{r}{c}{e}\right)}}}}}}}}$$
Given:
SST=13598.3,
SSR=3445.9,
$$\displaystyle{d}{f}_{{{\left(to{t}{a}{l}\right)}}}={29}$$
$$\displaystyle{d}{f}_{{{\left({s}{o}{u}{r}{c}{e}\right)}}}={1}$$
On substituting the values, the calculation for $$\displaystyle{S}_{{{e}}}$$ is as follows:
$$\displaystyle{S}_{{{e}}}=\sqrt{{{\frac{{{13598.3}-{3445.9}}}{{{29}-{1}}}}}}$$
$$\displaystyle=\sqrt{{{\frac{{{10152.4}}}{{{28}}}}}}$$
=19.042
Therefore, $$\displaystyle{S}_{{{e}}}={19.042}$$
Step 2
The formula of $$\displaystyle{r}^{{{2}}}={\frac{{{S}{S}{R}}}{{{S}{S}{T}}}}$$
Given:
SST=13598.3,
SSR=3445.9,
On substituting the values, the calculation for $$\displaystyle{R}^{{{2}}}$$ is as follows:
$$\displaystyle{r}^{{{2}}}={\frac{{{3445.9}}}{{{13598.3}}}}$$
=0.2534.
Therefore, $$\displaystyle{r}^{{{2}}}={0.2534}.$$
Step 3
The r is the square root of $$\displaystyle{r}^{{{2}}}$$. Take the square root of 0.2534 to obtain r.
$$\displaystyle{r}=\sqrt{{{0.2534}}}$$
=0.5034
Therefore, r=0.5034.