Consider the following data on price ($) and the overall score for six stereo headphones tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest).
(a) The estimated regression equation for this data is ŷ = 23.462 + 0.315x, where x = price ($) 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.)
(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.)
c) Show the ANOVA table for these data. (Round your p-value to three decimal places and all other values to two decimal places.)
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
Test statistics = 3.814
P-value = 0.0189
Test statistics = 15.54
P-value = 0.019
Analysis of variance table for regression model:
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