Question

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

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 + 0.315x,  where x = price (\$) and y = overall score. Does the t test indicate a significant relationship between price and the overall score? Use α = 0.05.

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

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

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

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