How to find combined SSE? For example, if we know that for a sample includes 107 income households, the SSE is 10.8. And for another sample including 98 income households, the SSE is 9.2. How to find the combined SSE for the all 225 samples?
 A: You need to look at the Chow statistic:
$$
F=\frac{SSR_p-(SSR_1+SSR_2)}{SSR_1+SSR_2} \cdot \frac{n-2(k+1)}{k+1}
$$
Where SSR is the sum of squared residuals (or errors if you prefer). K is the number of explanatory variables, n is the total sample. The subscript p refers to the model where you pool all observations, while 1 and 2 refer to the groups number. 
The trick about this question is to realize that you can work out $SSR_p$ from variance estimate in (a). Since the variance follows from:
$$
\sum_{i=1}^n \hat{u}_i^2 / (n-k-1) = s^2_u
$$
Where n and k has the same definition as above, and the sum of squared residuals are given by $\sum_{i=1}^n \hat{u}_i^2$.
The Chow test directly compares if there is difference in all the estimated parameters between the groups, which is what the question in (b) asked you verify. 
A: This is not a meaningful practice to calculate a combined SSE in my view- What are you trying to get out of that? You need to combine both sample first and fit one linear regression to the whole data space and then calculate the overall SSE, which accounts for the total error of your regression line to the fitted data.
A: In this context, the F-test is used to test whether the ratio of two SSE measures is equal to 1, in other words, whether the two SSE measures are equal:
$F_{(n_1-1, n_2-1)} = \frac{MSE_1}{MSE_2}$
Where $F$ is from the $F$-distribution with $n_1-1$ and $n_2-1$ degrees of freedom.
However, I don't think it is meaningful to compare $SSE_{low}$ and $SSE_{high}$ in such a way, because there would be little to learn from it and it doesn't answer the question. Usually in ANOVAs the $SSE_{variable}$ is compared to the $RSS$ (Residual Sum of Squares), but it is not immediately obvious where to find those in this problem.
