Question

On the first statistics exam, the coefficient of determination between the hours studied and the grade earned was 80%. The standard error of estimate was 10. There were 20 students in the class. Develop an ANOVA table for the regression analysis of hours studied as a predictor of the grade earned on the first statistics exam.

Answer 1

`\left[\begin{array}{ccccc}&DF&SS&MS&F\\Regression&1&7200&7200&72\\Error&18&1800&100\\total&19&900\end{array}\right]`

Step-by-step 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
`s_(y-x)=\sqrt {\frac {SSE}{n-2}}`

Here,
`SSE=(n-2)s_(y-x)^(2)=(20-2)(10)^(2)=1800`

Coefficient of determination
`r^(2)=\frac {SSE}{SS total}`

Here,
`SSR=r^(2)(SSR+SSE)`

`SSR=\frac {r^(2)}{1-r^(2)} SSE=\frac {0.8}{1-0.8}(1800)=7200`

The total sum of squares is

SS total=SSR+SSE=7200+1800=9000

MSR=SSR=7200

`MSE=\frac {SSE}{n-2}=\frac {1800}{20-2}=100`

F value is given by

`F=\frac {MSR}{MSE}=\frac {7200}{100}=100`

The ANOVA table is then

`\left[\begin{array}{ccccc}&DF&SS&MS&F\\Regression&1&7200&7200&72\\Error&18&1800&100\\total&19&900\end{array}\right]`