Consider the following set of ordered pairs. x 33 11 55 44 y 44 33 44...

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.

Solutions

Expert Solution

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

orchestra answered 1 year ago

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