Question

The following data show the brand, price ($), and the overall score for 6 stereo headphones that were tested by Consumer Reports. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is ŷ = 25.036 + 0.3x, where x = price ($) and y = overall score.

Brand Price Score Bose 180 76 Scullcandy 150 71 Koss 85 61 Phillips/O'Neill 70 57 Denon 70 30 JVC 45 35

Round your answers to three decimal places.

a. Compute SST, SSR, and SSE. SST SSR SSE

b. Compute the coefficient of determination r2. Comment on the goodness of fit. r2

c. What is the value of the sample correlation coefficient? r =

Answer 1

Independent variable (X) : Price

Dependent variable (Y); Score

Following table shows the calculations:

	X	Y	X^2	Y^2	XY
	180	76	32400	5776	13680
	150	71	22500	5041	10650
	85	61	7225	3721	5185
	70	57	4900	3249	3990
	70	30	4900	900	2100
	45	35	2025	1225	1575
Total	600	330	73950	19912	37180