Question

The following data show the brand, price ($), and the overall score for 6 stereo headphones that were tested by Consumer Reports. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is ŷ = 25.036 + 0.3x, where x = price ($) and y = overall score.

Brand Price Score Bose 180 76 Scullcandy 150 71 Koss 85 61 Phillips/O'Neill 70 57 Denon 70 30 JVC 45 35

Round your answers to three decimal places.

a. Compute SST, SSR, and SSE. SST SSR SSE

b. Compute the coefficient of determination r2. Comment on the goodness of fit. r2

c. What is the value of the sample correlation coefficient? r =

Answer #1

Independent variable (X) : Price

Dependent variable (Y); Score

Following table shows the calculations:

X | Y | X^2 | Y^2 | XY | |

180 | 76 | 32400 | 5776 | 13680 | |

150 | 71 | 22500 | 5041 | 10650 | |

85 | 61 | 7225 | 3721 | 5185 | |

70 | 57 | 4900 | 3249 | 3990 | |

70 | 30 | 4900 | 900 | 2100 | |

45 | 35 | 2025 | 1225 | 1575 | |

Total | 600 | 330 | 73950 | 19912 | 37180 |

The following data
show the brand, price ($), and the overall score for 6 stereo
headphones that were tested by Consumer Reports. The overall score
is based on sound quality and effectiveness of ambient noise
reduction. Scores range from 0 (lowest) to 100 (highest). The
estimated regression equation for these data is ŷ = 25.854 +
0.291x, where x = price ($) and y = overall score.
Brand
Price
Score
Bose
170
75
Scullcandy
160
71
Koss
95
62
Phillips/O'Neill...

Exercise 12.18
(Algorithmic)}
The following data
show the brand, price ($), and the overall score for 6 stereo
headphones that were tested by Consumer Reports. The overall score
is based on sound quality and effectiveness of ambient noise
reduction. Scores range from 0 (lowest) to 100 (highest). The
estimated regression equation for these data is ŷ = 28.381 +
0.266x, where x = price ($) and y = overall score.
Brand
Price
Score
Bose
180
75
Scullcandy
160
71
Koss...

The following data show the brand, price ($), and the overall
score for 6 stereo headphones that were tested by Consumer Reports.
The overall score is based on sound quality and effectiveness of
ambient noise reduction. Scores range from 0 (lowest) to 100
(highest). The estimated regression equation for these data is Y=
22.153 + 0.328 x, where x = price ($) and y = overall score. Brand
Price ($) Score Bose 170 76 Skullcandy 160 71 Koss 95 62...

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-hat = 25.147 + 0.299x , where x = price ( $ ) and y
= overall score.
Brand
Price
Score
Bose
180
75
Scullcandy...

The following data show the brand, price ($), and the overall
score for six stereo headphones that were tested by a certain
magazine. The overall score is based on sound quality and
effectiveness of ambient noise reduction. Scores range from 0
(lowest) to 100 (highest). The estimated regression equation for
these data is
ŷ = 19.385 + 0.346x,
where x = price ($) and y = overall score.
Brand
Price ($)
Score
A
180
78
B
150
71
C
95...

The following data show the brand, price ($), and the overall
score for six stereo headphones that were tested by a certain
magazine. The overall score is based on sound quality and
effectiveness of ambient noise reduction. Scores range from 0
(lowest) to 100 (highest). The estimated regression equation for
these data is
ŷ = 24.331 + 0.307x,
where x = price ($) and y = overall score.
Brand
Price ($)
Score
A
180
74
B
150
71
C
95...

The following data show the brand, price ($), and the overall
score for six stereo headphones that were tested by a certain
magazine. The overall score is based on sound quality and
effectiveness of ambient noise reduction. Scores range from 0
(lowest) to 100 (highest). The estimated regression equation for
these data is
ŷ = 22.324 + 0.327x,
where x = price ($) and y = overall score.
Brand
Price ($)
Score
A
180
78
B
150
69
C
95...

The following data show the brand, price ($), and the overall
score for six stereo headphones that were tested by a certain
magazine. The overall score is based on sound quality and
effectiveness of ambient noise reduction. Scores range from 0
(lowest) to 100 (highest). The estimated regression equation for
these data is
ŷ = 24.331 + 0.307x,
where x = price ($) and y = overall score.
Brand
Price ($)
Score
A
180
74
B
150
71
C
95...

The following data show the brand, price ($), and the overall
score for six stereo headphones that were tested by a certain
magazine. The overall score is based on sound quality and
effectiveness of ambient noise reduction. Scores range from 0
(lowest) to 100 (highest). The estimated regression equation for
these data is
ŷ = 21.656 + 0.333x,
where x = price ($) and y = overall score.
Brand
Price ($)
Score
A
180
76
B
150
73
C
95...

The following data show the brand, price ($), and the overall
score for six stereo headphones that were tested by a certain
magazine. The overall score is based on sound quality and
effectiveness of ambient noise reduction. Scores range from 0
(lowest) to 100 (highest). The estimated regression equation for
these data is
ŷ = 23.127 + 0.319x,
where x = price ($) and y = overall score.
Brand
Price ($)
Score
A
180
74
B
150
73
C
95...

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