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

Idilwsiw2 2021-11-19 Answered
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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Expert Answer

Kevin Hunt
Answered 2021-11-20 Author has 8812 answers

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.

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