The following data show the brand, price ($), and the overallscore for six stereo headphones that were tested by a certainmagazine. The overall score is based on sound quality andeffectiveness of ambient noise reduction. Scores range from 0(lowest) to 100 (highest). The estimated regression equation forthese data is
Å· = 23.659 + 0.323x,
where x = price ($) 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 decimalplaces.)
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 proportionof the variability in y has been explained by the leastsquares line.The least squares line provided a good fit as a largeproportion of the variability in y has been explained bythe least squares line.     The leastsquares line did not provide a good fit as a small proportion ofthe variability in y has been explained by the leastsquares line.The least squares line did not provide a good fit as alarge proportion of the variability in y has beenexplained by the least squares line.
(c)
What is the value of the sample correlation coefficient? (Roundyour answer to three decimal places.)
