The following data show the brand, price ($), and the overall score for 6 stereo

Question

The following data show the brand, price ($), and the overall score for 6 stereo headphones that were tested by consumer reports. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is y = 25.535 + 0.295x, where x = price ($) and y = overall score. a. Compute SST, SSR, and SSE. SST 1793.5 SSR 1354.51 SSE b. Compute the coefficient of determination r^2. Comment on the goodness of fit. r^2 = 86 c. What is the value of the sample correlation coefficient? r = 6

Explanation / Answer

From the given data

SST = 1720

SSR = 1297.928

SSE = 722.0719

b)

r2 = 1297.928/1720 = 0.75461

c) r = 0.86868

X Y Y-Cap (Y-Ycap)^2 (Yi-Ybar)^2 (Ybar-Ycap)^2 180 76 78.5719064 6.6147023 441 555.6347692 150 71 69.7324415 1.60670462 256 217.0448317 95 61 53.5267559 55.8493781 36 2.170448317 70 56 46.1605351 96.8150692 1 78.13613942 70 30 46.1605351 261.162895 625 78.13613942 35 36 35.8478261 0.0231569 361 366.8057656 Total : 600 330 422.071906 1720 1297.928094

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