Question

Given are five observations for two variables,  and .

	3	6	12	17	20
	59	54	47	14	16

The estimated regression equation for these data is y = 70.84 - 2.83x

a. Compute SST, SSE , and SSR.

	(to 2 decimals)
	(to 2 decimals)
	(to 2 decimals)

b. Compute the coefficient of determination r^2. Comment on the goodness of fit.

(to 3 decimals)

The least squares line provided an - Select your answer -goodbadItem 5 fit;   of the variability in  has been explained by the estimated regression equation (to 1 decimal).

c. Compute the sample correlation coefficient. Enter negative value as negative number.

(to 3 decimals)

Answer 1

For the given data using Regression Excel we get output as

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.94605133
R Square	0.895013119
Adjusted R Square	0.860017492
Standard Error	8.0200974
Observations	5
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1645.034113	1645.034	25.574999	0.014919662
Residual	3	192.9658869	64.32196
Total	4	1838
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	70.84405458	7.419134087	9.548831	0.0024363	47.23305872	94.45505044
x	-2.831384016	0.559874857	-5.05717	0.0149197	-4.613155685	-1.049612346

( c )  sample correlation coefficient.

Find X⋅Y , X² and Y² as it was done in the table below.

X	Y	X⋅Y	X⋅X	Y⋅Y
3	59	177	9	3481
6	54	324	36	2916
12	47	564	144	2209
17	14	238	289	196
20	16	320	400	256

r = -0.946