Question

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 + 0.327* x*,

where *x* = price ($) and *y* = overall score.

Brand | Price ($) | Score |
---|---|---|

A | 180 | 78 |

B | 150 | 69 |

C | 95 | 61 |

D | 70 | 58 |

E | 70 | 40 |

F | 35 | 24 |

(a)

Compute SST, SSR, and SSE. (Round your answers to three decimal places.)

SST=SSR=SSE=

(b)

Compute the coefficient of determination

*r*^{2}.

(Round your answer to three decimal places.)

*r*^{2}

=

Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.)

The least squares line provided a good fit as a small proportion
of the variability in *y* has been explained by the least
squares line.The least squares line did not provide a good fit as a
large proportion of the variability in *y* has been
explained by the least squares line. The
least squares line did not provide a good fit as a small proportion
of the variability in *y* has been explained by the least
squares line.The least squares line provided a good fit as a large
proportion of the variability in *y* has been explained by
the least squares line.

(c)

What is the value of the sample correlation coefficient? (Round your answer to three decimal places.)

Answer #1

The statistical software output for this problem is :

SST = 1956

SSR = 1596.202

SSE = 359.798

r ^{2} = 0.816

The least squares line provided a good fit as a small proportion
of the variability in *y* has been explained by the least
squares line.

sample correlation coefficient = 0.903

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...

The following data show the brand, price ($), and the overall
score for six stereo headphones that were tested by a certain
magazine. The overall score is based on sound quality and
effectiveness of ambient noise reduction. Scores range from 0
(lowest) to 100 (highest). The estimated regression equation for
these data is ŷ = 25.465 + 0.305x, where x = price ($) and y =
overall score.
Brand Price ($) Score
A 180 78
B 150 69
C 95...

The following data show the brand, price ($), and the overall
score for six stereo headphones that were tested by a certain
magazine. The overall score is based on sound quality and
effectiveness of ambient noise reduction. Scores range from 0
(lowest) to 100 (highest). The estimated regression equation for
these data is
ŷ = 23.528 + 0.315x,
where x = price ($) and y = overall score.
Brand
Price ($)
Score
A
180
76
B
150
71
C
95...

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

Consider the data.
xi
3
12
6
20
14
yi
65
35
50
15
20
The estimated regression equation for these data is
ŷ = 70 − 3x.
(a)
Compute SSE, SST, and SSR using equations
SSE = Σ(yi −
ŷi)2,
SST = Σ(yi −
y)2,
and
SSR = Σ(ŷi −
y)2.
SSE = SST = SSR =
(b)
Compute the coefficient of determination
r2.
(Round your answer to three decimal places.)
r2
=
Comment on the goodness of fit....

Consider the data.
xi
1
2
3
4
5
yi
3
7
4
10
12
The estimated regression equation for these data is
ŷ = 0.90 + 2.10x.
(a)
Compute SSE, SST, and SSR using equations
SSE = Σ(yi −
ŷi)2,
SST = Σ(yi −
y)2,
and
SSR = Σ(ŷi −
y)2.
SSE=SST=SSR=
(b)
Compute the coefficient of determination
r2.
r2
=
Comment on the goodness of fit. (For purposes of this exercise,
consider a proportion large if it is...

Consider the data.
xi
1
2
3
4
5
yi
3
7
5
11
14
The estimated regression equation for these data is
ŷ = 0.20 + 2.60x.
(a)
Compute SSE, SST, and SSR using equations
SSE = Σ(yi −
ŷi)2,
SST = Σ(yi −
y)2,
and
SSR = Σ(ŷi −
y)2.
SSE = SST = SSR =
(b)
Compute the coefficient of determination
r2.
r2
=
Comment on the goodness of fit. (For purposes of this exercise,
consider a...

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