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 + 0.315x,  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.)

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