Question

Consider the following data on price ($) and the overall score for six stereo headphones 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).

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

A | 180 | 76 |

B | 150 | 69 |

C | 95 | 63 |

D | 70 | 58 |

E | 70 | 40 |

F | 35 | 24 |

(a) The estimated regression equation for this data is
*ŷ* = 23.462 + 0.315* x*, where

Find the value of the test statistic. (Round your answer to three decimal places.)

Find the *p*-value. (Round your answer to four decimal
places.)

*p*-value

(b) Test for a significant relationship using the *F*
test. Use α = 0.05.

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the *p*-value. (Round your answer to three decimal
places.)

*p*-value =

c) Show the ANOVA table for these data. (Round your
*p*-value to three decimal places and all other values to
two decimal places.)

Source of Variation |
Sum of Squares |
Degrees of Freedom |
Mean Square |
F |
p-value |
---|---|---|---|---|---|

Regression | |||||

Error | |||||

Total |

Answer #1

The statistic software output for this problem is :

Simple linear regression results:

Dependent Variable: Score

Independent Variable: Price ($)

Score = 23.461538 + 0.31538462 Price ($)

Sample size: 6

R (correlation coefficient) = 0.88560882

R-sq = 0.78430299

Estimate of error standard deviation: 10.111399

Parameter estimates:

Parameter | Estimate | Std. Err. | Alternative | DF | T-Stat | P-value |
---|---|---|---|---|---|---|

Intercept | 23.461538 | 9.2427421 | ≠ 0 | 4 | 2.5383742 | 0.0641 |

Slope | 0.31538462 | 0.082697169 | ≠ 0 | 4 | 3.8137293 | 0.0189 |

(a)

Test statistics = 3.814

P-value = 0.0189

(b)

Test statistics = 15.54

P-value = 0.019

(c)

Analysis of variance table for regression model:

Source | DF | SS | MS | F-stat | P-value |
---|---|---|---|---|---|

Model | 1 | 1487.04 | 1487.04 | 14.54 | 0.019 |

Error | 4 | 408.96 | 102.24 | ||

Total | 5 | 1896 |

Consider the following data on price ($) and the overall score
for six stereo headphones tested by a certain magazine. The overall
score is based on sound quality and effectiveness of ambient noise
reduction. Scores range from 0 (lowest) to 100 (highest).
Brand
Price ($)
Score
A
180
78
B
150
71
C
95
63
D
70
58
E
70
38
F
35
28
(a) The estimated regression equation for this data is ŷ =
24.060 + 0.319x, where x...

Consider the following data on price ($) and the overall score
for six stereo headphones tested by a certain magazine. The overall
score is based on sound quality and effectiveness of ambient noise
reduction. Scores range from 0 (lowest) to 100 (highest).
Brand
Price ($)
Score
A
180
74
B
150
71
C
95
63
D
70
54
E
70
38
F
35
24
(a)
The estimated regression equation for this data is
ŷ = 21.659 + 0.323x,
where x...

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 on price ($) and the overall score for 6
stereo headphones that were tested by Consumer Reports were as
follows.
Brand
Price
Score
Bose
180
76
Scullcandy
160
77
Koss
95
63
Phillips/O'Neill
70
56
Denon
80
50
JVC
35
26
a. Does the t test indicate a significant
relationship between price and the overall score?
The test t-Conclusion at α = .05
t = (to 2 decimal places.)
p-value is - Select your answer -less than .02between...

The following data on price ($) and the overall score for 6
stereo headphones that were tested by Consumer Reports were as
follows.
Brand
Price
Score
Bose
190
78
Scullcandy
150
76
Koss
85
67
Phillips/O'Neill
80
57
Denon
80
40
JVC
45
27
a. Does the t test indicate a significant
relationship between price and the overall score?
The test t-Conclusion at α = .05
t = (to 2 decimal places.)
p-value is - Select your answer -less than .02,...

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...

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...

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