Question

The following data show the brand, price ($), and the overall score for 6 stereo headphones that were tested by Consumer Reports. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is = 24.881 + 0.301 x, where x = price ($) and y = overall score. Brand Price ($) Score Bose 180 75 Scullcandy 160 72 Koss 95 61 Phillips/O'Neill 70 56 Denon 60 40 JVC 35 26 Round your answers to three decimal places. a. Compute SST, SSR, and SSE. SST SSR SSE b. Compute the coefficient of determination r 2. Comment on the goodness of fit. r 2 = SelectThe least squares line provided a very good fitThe least squares line provided a bad fit c. What is the value of the sample correlation coefficient? r =

Answer 1

using Minitab >stat>basic stat>Regression

Regression Analysis: Score versus Price ($)

The regression equation is
Score = 24.88 + 0.3012 Price ($)

S = 8.25343 R-Sq = 84.8% R-Sq(adj) = 81.0%

Analysis of Variance

Source DF SS MS F P
Regression 1 1519.52 1519.52 22.31 0.009
Error 4 272.48 68.12
Total 5 1792.00

a. Compute SST, SSR, and SSE.

SST	1792
SSR	1519.52
SSE	272.48

b. the coefficient of determination r ²

r ² = 84.8%

the least squares line provided a very good fit

c. the sample correlation coefficient is

r =0.921