The following data show the brand, price ($), and the overall score for six stereo headphones that were tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is
ŷ = 24.331 + 0.307x,
where x = price ($) and y = overall score.
Brand | Price ($) | Score |
---|---|---|
A | 180 | 74 |
B | 150 | 71 |
C | 95 | 63 |
D | 70 | 58 |
E | 70 | 38 |
F | 35 | 26 |
(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 =
(c) What is the value of the sample correlation coefficient? (Round your answer to three decimal places.)
The statistic software output for this problem is :
(a)
SST = 1820
SSR = 1406.169
SSE = 413.831
(b)
r 2 = 0.773
(c)
The value of the sample correlation coefficient = 0.879
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