Question

step 4 of 4: find the mean square for error, mse. round your answer to four decimal places. sst ≈ 13.1818 sse ≈ 812.5455

Explanation:

Step1: Recall MSE formula

The formula for the mean - square error (MSE) in the context of ANOVA is $MSE=\frac{SSE}{n - k}$, where $SSE$ is the sum - of - squares due to error and $n - k$ is the degrees of freedom for error. However, the degrees of freedom are not given in the problem. Assuming a one - way ANOVA situation where we are not given the number of groups ($k$) and total number of observations ($n$), if we assume that the necessary degrees of freedom for error calculation are already accounted for in a general sense and we are just given the $SSE$ value directly related to the MSE calculation, we can use the fact that $MSE=\frac{SSE}{df_{error}}$. In a simple case where we are just given $SSE$ and no other information about degrees of freedom related calculations, if we assume the appropriate degrees of freedom are already incorporated in the way $SSE$ is presented for MSE calculation, we can use the formula $MSE = \frac{SSE}{df}$. Since no other information is given, we assume a situation where we can directly calculate $MSE$ as $MSE=\frac{SSE}{df}$. Here, we assume the relevant $df$ is 1 (a very simplistic view when no other details are provided). In a more proper ANOVA context, we would need more information about the data structure. But based on the given $SSE$ value for direct MSE calculation as presented in the problem, we have:
$MSE=\frac{SSE}{df}$

Step2: Substitute values

We are given $SSE\approx812.5455$. Let's assume the degrees of freedom for error ($df$) is 1 (as no other information is given). Then $MSE=\frac{812.5455}{1}=812.5455$

Answer:

$812.5455$