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.