Consider the following Excel regression of perceived sound quality as a function

Question

Consider the following Excel regression of perceived sound quality as a function of price for 27 stereo speakers.

(a) Is the coefficient of Price significantly different from zero at = .05?

(b) What does the R2 tell you?

(c) Given these results, would you conclude that a higher price implies higher sound quality?

Regression Statistics

R Square

0.01104

Standard Error

4.02545

Observations

        27

Statistic

Coefficients

Std Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

88.4902

1.67814

52.731

0.0000

85.0340

91.9464

Price

0.00239

0.00453

0.528

0.6019

0.01172

0.00693

Regression Statistics

R Square

0.01104

Standard Error

4.02545

Observations

        27

Explanation / Answer

a) since p-value of price is 0.6019 > 0.05
we fail to reject the null hypothesis
hence the coefficient of Price significantly is not different from zero at = .05

b)
R^2 = 0.0114
this model accounts for 1.1 % of variation in dependent variable

c)
we see that slope is negative , which suggest that higher price implies lower sound quality
but the variable is not significant
so we can't conclude that higher price implies higher sound quality

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