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 α = .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
(a) significant difference the -pvalue 0.6019 > 0.05 table value for t stat at alpha 0.05 < -0.528 calculated tstat value
(b) R2 is a percentage between 0-100 We have R2 of 1.104% and since it is a measure of response around the mean we can conclude there are only small differences along the regression line ( i feel i need to dd more here to finish the sentenceor will this be sufficient?)
(c) So this is where i feel i am most stuck, bare with me - If the R2 value is low, and shows only small differences along the regression line then it means buying a higher priced speaker will give better sound quality? but not by much or am I way off here?