We need to complete the ANOVA table for a simple linear regression. We are given the following information: - SS(Model) = 44.21 - SS(Total) = 66.12 - df(Total) = 44 We need to find: - SS(Error) - df(Model) - df(Error) - MS(Model) - MS(Error) - F

1. Problem Description

We need to complete the ANOVA table for a simple linear regression. We are given the following information:

- SS(Model) = 44.21

- SS(Total) = 66.12

- df(Total) = 44

We need to find:

- SS(Error)

- df(Model)

- df(Error)

- MS(Model)

- MS(Error)

- F

2. Solution Steps

First, we calculate SS(Error).

$SS_{Total} = SS_{Model} + SS_{Error}$

$SS_{Error} = SS_{Total} - SS_{Model}$

$SS_{Error} = 66.12 - 44.21 = 21.91$

Next, we find df(Model). For a simple linear regression, the degrees of freedom for the model is always

1. $df_{Model} = 1$

Then we find df(Error).

$df_{Total} = df_{Model} + df_{Error}$

$df_{Error} = df_{Total} - df_{Model}$

$df_{Error} = 44 - 1 = 43$

Now we calculate MS(Model).

$MS_{Model} = \frac{SS_{Model}}{df_{Model}}$

$MS_{Model} = \frac{44.21}{1} = 44.21$

We calculate MS(Error).

$MS_{Error} = \frac{SS_{Error}}{df_{Error}}$

$MS_{Error} = \frac{21.91}{43} \approx 0.51$

Finally, we calculate the F statistic.

$F = \frac{MS_{Model}}{MS_{Error}}$

$F = \frac{44.21}{0.51} \approx 86.69$

3. Final Answer

Source | SS | df | MS | F

-------|-------|----|--------|--------

Model | 44.21 | 1 | 44.21 | 86.69

Error | 21.91 | 43 | 0.51 |

Total | 66.12 | 44 | |