Question

In: Statistics and Probability

1.-The following data were used in a regression study. Observation 1 2 3 4 5 6...

1.-The following data were used in a regression study.

Observation 1 2 3 4 5 6 7 8 9

xi

2 3 4 5 7 7 7 8 9

yi

4 5 4 7 4 6 9 6 11

(a)Develop an estimated regression equation for these data. (Round your numerical values to two decimal places.)

ŷ =______

2.-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 = 20.987 + 0.340x, where x = price ($) and y = overall score.

Brand Price ($) Score
A 180 78
B 150 73
C 95 59
D 70 54
E 70 40
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.)____

Solutions

Expert Solution

1)

= 2.36 + 0.67 x

2)

(a)

SST = 1936

SSR = 1729.580

SSE = 206.420

(b)

r 2 = 0.893

(c)

The value of the sample correlation coefficient = r = 0.945


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