The following data show the brand, price , and the overall score for stereo headphones that were...

The following data show the brand, price , and the overall score for stereo headphones that were tested by Consumer Reports. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from (lowest) to (highest). The estimated regression equation for these data is ^y=23.638+0.314x, where x=price and y=score

Brand	Price	Score
Bose	180	75
Scullcandy	150	72
Koss	85	61
Phillips/O'Neill	70	56
Denon	70	40
JVC	45	26

Round your answers to three decimal places.

a. Compute SST,SSR ,SSE and .

SST		(to 3 decimals)
SSR		(to 3 decimals)
SSE		(to 3 decimals)

b. Compute the coefficient of determination r^2.

Comment on the goodness of fit.

c. What is the value of the sample correlation coefficient?

Solutions

Expert Solution

Solution: We can use the excel regression data analysis tool to find the answers to the given questions. The excel output is given below:

a. Compute SST,SSR ,SSE

Answer:

SST	1792
SSR	1372.088
SSE	419.912

b. Compute the coefficient of determination r^2.

Comment on the goodness of fit.

Answer: . Therefore, 76.6% of the variation in the score is explained by the price.

c. What is the value of the sample correlation coefficient?

Answer: The value of the sample correlation coefficient is:

orchestra answered 1 year ago

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