Question
In: Statistics and Probability
The following data show the brand, price , and the overall score for stereo headphones that were...
The following data show the brand, price , and the overall score for 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 (lowest) to (highest). The estimated regression equation for these data is ^y=23.638+0.314x, where x=price and y=score
| Brand | Price | Score |
| Bose | 180 | 75 |
| Scullcandy | 150 | 72 |
| Koss | 85 | 61 |
| Phillips/O'Neill | 70 | 56 |
| Denon | 70 | 40 |
| JVC | 45 | 26 |
Round your answers to three decimal places.
a. Compute SST,SSR ,SSE and .
| SST | (to 3 decimals) | |
| SSR | (to 3 decimals) | |
| SSE | (to 3 decimals) |
b. Compute the coefficient of determination r^2.
Comment on the goodness of fit.
c. What is the value of the sample correlation coefficient?
Solutions
Expert Solution
Solution: We can use the excel regression data analysis tool to find the answers to the given questions. The excel output is given below:
a. Compute SST,SSR ,SSE
Answer:
| SST | 1792 |
| SSR | 1372.088 |
| SSE | 419.912 |
b. Compute the coefficient of determination r^2.
Comment on the goodness of fit.
Answer: 
.
Therefore, 76.6% of the variation in the score is explained by the
price.
c. What is the value of the sample correlation coefficient?
Answer: The value of the sample correlation coefficient is:
orchestra answered 2 years agoRelated Solutions
The following data show the brand, price , and the overall score for stereo headphones that were...
The following data show the brand, price , and the overall score
for 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 (lowest) to (highest). The estimated
regression equation for these data is ^y=23.638+0.314x, where
x=price and y=score
Brand
Price
Score
Bose
180
75
Scullcandy
150
72
Koss
85
61
Phillips/O'Neill
70
56
Denon
70
40
JVC
45
26
Round your answers to three decimal places.
a....
The following data show the brand, price , and the overall score for stereo headphones that were...
The following data show the brand, price , and the overall score
for 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 (lowest) to (highest). The estimated
regression equation for these data is ,
where and .
Brand
Price
Score
Bose
180
76
Scullcandy
150
71
Koss
95
62
Phillips/O'Neill
70
57
Denon
60
30
JVC
45
34
Round your answers to three decimal places.
a. Compute SST, SSR,...
The following data show the brand, price, and the overall score for six stereo headphones that...
The following data show the brand, price, and the overall score
for six 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 to 100.
Price Score
Bose 180 76
Skullcandy 150 71
Koss 85 61
Phillips/O'Neill 70 56
Denon 70 40
JVC 35 26
a). Develop the estimated regression equation that could be used
to predict the score given the price.
b). Compute...
The following data show the brand, price ($), and the overall score for six stereo headphones...
The following data show the brand, price ($), 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 = 23.462 + 0.315x,
where x = price ($) and y = overall score.
Brand
Price ($)
Score
A
180
74
B
150
73
C
95...
The following data show the brand, price ($), and the overall score for 6 stereo headphones...
The following data show the brand, price ($), 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 = 23.395 + 0.316 x, where
x = price ($) and y = overall score.
Brand
Price ($)
Score
Bose
180
75
Scullcandy
150
72
Koss
95
61
Phillips/O'Neill...
The following data show the brand, price ($), and the overall score for six stereo headphones...
The following data show the brand, price ($), 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 = 19.786 +
0.342x, where x = price ($) and
y = overall score.
Brand
Price ($)
Score
A
180
76
B
150
73
C
95
59...
The following data show the brand, price ($), and the overall score for 6 stereo headphones...
The following data show the brand, price ($), 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 = 20.397 + 0.346 x, where
x = price ($) and y = overall score.
Brand
Price ($)
Score
Bose
170
75
Scullcandy
150
72
Koss
95
62
Phillips/O'Neill...
The following data show the brand, price ($), and the overall score for six stereo headphones...
The following data show the brand, price ($), 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 = 23.194 + 0.318x,
where x = price ($) and y = overall score.
Brand
Price ($)
Score
A
180
76
B
150
71
C
95...
The following data show the brand, price ($), and the overall score for six stereo headphones...
The following data show the brand, price ($), 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 = 21.258 + 0.327x,
where x = price ($)and y = overall score.
Brand
Price ($)
Score
A
180
76
B
150
69
C
95
63...
The following data show the brand, price ($), and the overall score for six stereo headphones...
The following data show the brand, price ($), 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 = 23.659 + 0.323x,
where x = price ($) and y = overall score.
Brand
Price ($)
Score
A
180
78
B
150
73
C
95...
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