Question

The following data show the brand, price ($), and the overall score for six stereo headphones that were tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is

ŷ = 23.659 + 0.323x,

where x = price ($) and y = overall score.

Brand	Price ($)	Score
A	180	78
B	150	73
C	95	59
D	70	58
E	70	40
F	35	28

(a)

Compute SST, SSR, and SSE. (Round your answers to three decimal places.)

SST = SSR = SSE =

(b)

Compute the coefficient of determination

r².

(Round your answer to three decimal places.)

r²

=

Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.)

The least squares line provided a good fit as a small proportion of the variability in y has been explained by the least squares line.The least squares line provided a good fit as a large proportion of the variability in y has been explained by the least squares line.     The least squares line did not provide a good fit as a small proportion of the variability in y has been explained by the least squares line.The least squares line did not provide a good fit as a large proportion of the variability in y has been explained by the least squares line.

(c)

What is the value of the sample correlation coefficient? (Round your answer to three decimal places.)

Answer 1

Solution: We can use the excel regression data analysis tool to find the answer to the given questions. The excel output is given below:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.9254
R Square	0.8563
Adjusted R Square	0.8204
Standard Error	8.0979
Observations	6
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1563.6940	1563.6940	23.8453	0.0081
Residual	4	262.3060	65.5765
Total	5	1826
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	23.6589	7.4022	3.1962	0.0330	3.1069	44.2108
Price ($)	0.3234	0.0662	4.8832	0.0081	0.1395	0.5073

(a) Compute SST, SSR, and SSE. (Round your answers to three decimal places.)

Answer:

(b) Compute the coefficient of determination r².

Answer:

Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.)

Answer: The least squares line provided a good fit as a large proportion of the variability in y has been explained by the least-squares line.

(c) What is the value of the sample correlation coefficient?

Answer: