Question

1 3 4

Sum of residual squares

Answer 1

Following table shows the calculations:

	X	Y	X^2	Y^2	XY
	-2	4	4	16	-8
	-1	3	1	9	-3
	0	3	0	9	0
	1	1	1	1	1
	2	-1	4	1	-2
Total	0	10	10	36	-12

Sample size: n=5

$S_{yy}=\sum y^{2}-\frac{\left (\sum y \right )^{2}}{n}=16$

$S_{xx}=\sum x^{2}-\frac{\left (\sum x \right )^{2}}{n}=10$

$S_{xy}=\sum xy-\frac{\left (\sum x \right )\left (\sum y \right )}{n}=-12$

The SSE is

$SSE=S_{yy}-\frac{S^{2}_{xy}}{S_{xx}}=1.6$

The s^2 is

$s^{2}=\frac{SSE}{n-2}=\frac{1.6}{3}=0.5333$

So standard error of estimate will be

$s=\sqrt{\frac{SSE}{n-2}}=\sqrt{\frac{1.6}{3}}=0.7303$

The sum of residual squares:

$SSR=\frac{S^{2}_{xy}}{S_{xx}}=14.4$