Question

The following data show the brand, price ($), and the overall score for 6 stereo headphones that were tested by Consumer Reports. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is û 24.9 +0.301c , where = price ($) and y overall score. Brand Price Score Bose 180 76 Scullcandy 150 71 Koss 95 62 Phillips/O'Neill 70 57 Denon 70 30 JVC 35 34 Round your answers to three decimal places. a. Compute SST, SSR, and SSE. (to 3 decimals) SST (to 3 decimals) SSR (to 3 decimals) SSE b. Compute the coefficient of determination r2 Comment on the goodness of fit. The input in the box below will not be graded, but may be reviewed and considered by your instructor. blank c. What is the value of the sample correlation coefficient?

Answer 1

Y Values X-M₂ Y-My (X-M2 X Values 180 150 95 6400 (X-MXXY-M) 1680 800 2500 25 -35 900 900 4225 -60 750 1365 M: 100 M: 55 SS: 14950 SP: 4500 a. The required values are: SST = SS, =Z(Y - M,)? = 212 +162 +72+ 2? +(-25) +(-21)? =1816 SSR = o SP2 45002 =1354.5 SSB 14950 SSE = SST - SSR =1816-1354.5 = 461.5

b. The coefficient of determination is, Explained Variation Total Variation SSR SST 1354.5 1816 = 0.7458 This means that 74.58% o9f variation in y can be explained by variation in x. c. The value of the sample correlation coefficient is, = 0.7458 = 0.8635 The obtained correlation coefficient indicates a strong positive correlation between x and y.