Question

Exercise 12.18 (Algorithmic)}

The following data show the brand, price ($), and the overall score for 6 stereo headphones that were tested by Consumer Reports. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is ŷ = 28.381 + 0.266x, where x = price ($) and y = overall score.

Brand	Price	Score
Bose	180	75
Scullcandy	160	71
Koss	95	61
Phillips/O'Neill	70	57
Denon	70	30
JVC	25	36

Round your answers to three decimal places.

a. Compute SST, SSR, and SSE.

SST
SSR
SSE

b. Compute the coefficient of determination r². Comment on the goodness of fit.

r² =

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

r =

Answer 1

We can use here Excel for regression equation

Step 1) Enter data in Excel .

Step 2) Data >>Data analysis >>Regression >>Select y and x values separately >>Ok
a)

SST=1682
SSR=1236.448
SSE=445.552

b)

r^2 = 0.735

Therefore, 73.5% of the variation in dependent variable can be explained by the variation in independent variable.

model is good enough for fit.

c)  

r=0.857