Question

The following data show the brand, price ($), and the overall score for six stereo headphones that were tested by a certain magazine. 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 = 21.258 + 0.327x,

where x = price ($)and y = overall score.

Brand	Price ($)	Score
A	180	76
B	150	69
C	95	63
D	70	54
E	70	38
F	35	24

(a)

Compute SST (Total Sum of Squares), SSR (Regression Sum of Squares), and SSE (Error Sum of Squares). (Round your answers to three decimal places.)

SST=SSR=SSE=

(b)

Compute the coefficient of determination

r².

(Round your answer to three decimal places.)

r²

=

Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.)

The least squares line provided a good fit as a large proportion of the variability in y has been explained by the least squares line.The least squares line did not provide a good fit as a small proportion of the variability in y has been explained by the least squares line.    The least squares line provided a good fit as a small proportion of the variability in y has been explained by the least squares line.The least squares line did not provide a good fit as a large proportion of the variability in y has been explained by the least squares line.

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=1946

SSR=1602.744

SSE=343.256

b)

The coefficient of determination

Therefore, 82.4% of the variation in dependent variable can be explained by the variation in independent variable.

The least squares line provided a good fit as a large proportion of the variability in y has been explained by the least squares line.