In: Statistics and Probability
30.
The following data show the brand, price ($), and the overall
score for 6 stereo headphones that were tested by Consumer Reports.
The overall score is based on sound quality and effectiveness of
ambient noise reduction. Scores range from 0 (lowest) to 100
(highest). The estimated regression equation for these data is ŷ =
23.185 + 0.318x, where x = price ($) and y = overall
score.
Brand | Price | Score |
Bose | 170 | 76 |
Scullcandy | 160 | 71 |
Koss | 95 | 62 |
Phillips/O'Neill | 60 | 57 |
Denon | 70 | 40 |
JVC | 45 | 24 |
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 =
The statistical software output for this problem is :
SST = 1936
SSR = 513.872
SSE = 513.872
r 2 = 0.735
r = 0.857