Question

The following data show the brand, price ($), and the overall score for six stereo headphones that were tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is ŷ = 25.465 + 0.305x, where x = price ($) and y = overall score.

Brand Price ($) Score

A 180 78

B 150   69

C 95 61

D 70 58

E 70 42

F 35 28

(a) Compute SST, SSR, and SSE. (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 =

(For purposes of this exercise, consider a proportion large if it is at least 0.55.)

1. 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.

2. 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.

3. 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.

4. 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.

(c) What is the value of the sample correlation coefficient? (Round your answer to three decimal places.)

Answer 1

a)

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	600.00	336.00	14950.00	1662.00	4565.00
mean	100.00	56.00	SSxx	SSyy	SSxy

SSE=   (SSxx * SSyy - SS²xy)/SSxx =    268.0719

SSR=   S²xy/Sxx =   1393.9281

Ssyy=   SST = 1662

b)

R² =    1-SSE/SST =    0.8387

3. 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.

c)

SSE=   (SSxx * SSyy - SS²xy)/SSxx =    268.0719
std error ,Se =    √(SSE/(n-2)) =    8.1865
      
correlation coefficient ,    r = SSxy/√(SSx.SSy) =   0.916

Please let me know in case of any doubt.

Thanks in advance!

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