Answer:
[tex]\left[\begin{array}{ccccc}&DF&SS&MS&F\\Regression&1&7200&7200&72\\Error&18&1800&100\\total&19&900\end{array}\right][/tex]
Explanation:
Sample size, n=20
Degrees of freedom is 1
Number of degrees of freedom for error is n-2 hence 20-2=18
Total number of degrees of freedom is 18+1=19
Standard error estimate is [tex]s_{y-x}=\sqrt {\frac {SSE}{n-2}}[/tex]
Here, [tex]SSE=(n-2)s_{y-x}^{2}=(20-2)(10)^{2}=1800[/tex]
Coefficient of determination [tex]r^{2}=\frac {SSE}{SS total}[/tex]
Here, [tex]SSR=r^{2}(SSR+SSE) [/tex]
[tex]SSR=\frac {r^{2}}{1-r^{2}} SSE=\frac {0.8}{1-0.8}(1800)=7200[/tex]
The total sum of squares is
SS total=SSR+SSE=7200+1800=9000
MSR=SSR=7200
[tex]MSE=\frac {SSE}{n-2}=\frac {1800}{20-2}=100[/tex]
F value is given by
[tex]F=\frac {MSR}{MSE}=\frac {7200}{100}=100[/tex]
The ANOVA table is then
[tex]\left[\begin{array}{ccccc}&DF&SS&MS&F\\Regression&1&7200&7200&72\\Error&18&1800&100\\total&19&900\end{array}\right][/tex]