Question

Consider the following set of ordered pairs.

x	33	11	55	44
y	44	33	44	44

​a) Calculate the slope and​ y-intercept for these data.

​b) Calculate the total sum of squares​ (SST).

​c) Partition the sum of squares into the SSR and SSE.

Answer 1

For the given data using Regression in Excel we get output as

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.878310066
R Square	0.771428571
Adjusted R Square	0.657142857
Standard Error	0.292770022
Observations	4
ANOVA
	df	SS	MS	F	Significance F
Regression	1	0.578571429	0.578571	6.75	0.121689934
Residual	2	0.171428571	0.085714
Total	3	0.75
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	2.914285714	0.353409054	8.246211	0.014389	1.393689285	4.43488214
x	0.257142857	0.098974332	2.598076	0.12169	-0.168709322	0.68299504

From the above output

( a )

Slope = 0.25714

Y intercept = 2.91429

( b )

total sum of squares​ (SST ) = 0.75

( c )

SSR =  0.578571429

SSE = 0.171428571

Partition the sum of squares into the SSR and SSE.

• SST = SSR + SSE
• 0.75 =  0.578571429 + 0.171428571