Consider the following Excel regression of perceived sound quality as a function
ID: 3353514 • Letter: C
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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