Question

The following data show the brand, price (S), and the overall score for 6 stereo headphones that were tested by Consumer Reports. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from O (lowest) to 10° (highest). The estimated regression euation for these data is ,-2S857·0291x,-here x-price (s) and y " overall score. Price Score 76 71 61 160 85 70 60 45 Koss 30 35 VC Round your answers to three decimal places a. Compute SST,SSR, and SSE SST SSE b. Compute the coefficient of determination Comment on the goodness of fit c. What is the value of the sample correlation coefficient?

Answer 1

1)

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.871303492
R Square	0.759169775
Adjusted R Square	0.698962218
Standard Error	10.29979195
Observations	6
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1337.657143	1337.657143	12.60921088	0.0237784
Residual	4	424.3428571	106.0857143
Total	5	1762
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	25.85714286	9.221548756	2.803991341	0.048613431	0.25401895
x	0.291428571	0.082070707	3.550945069	0.0237784	0.06356376

SST	1762
SSR	424.3428571
SSE	1337.657143
b)
R^2	0.759169775
	This is moderate fit
c)
r	0.871303492