I'm a BC student who is trying to solve some statistic quizzes.
there is a multiple choice question that is this:
In a simple regression model $y=a+bx+e$ our given data is this: $$ \bar{x} = 2, \bar{y} = 3, S_x = 4, S_y = 5, r = 0.6 $$ find SSE and $S_{y,x}$.
- $16, 4$
- $14, 4$
- $4, 14$
- $4, 16$
I must confess I have no idea what is a $S_{y,x}$! but for SSE here is my work (I've assumed that $s_y$ is the sum of all $y$):
\begin{align} \text{SSE} = (1-r^2) \text{SST} &= (1-r^2)\sum(y-\bar y)^2 \\ &= (1-r^2) \left(\sum y^2 -\frac{(\sum y)^2}n \right) \\ &= (1-r^2)\left(\sum y^2 -\frac{S^2_y}n \right) \\ &= (1-r^2)\left( \sum y^2 -\frac{S^2_y}{\left. S_y \middle/ \bar y \right.} \right) \\ &= (1-r^2)\left( \sum y^2 -S_y \bar y \right) \end{align}
but in this case, I can't find $\sum y^2$. I want some help.
thank in advance.