The following data show the brand, price ($), and the overall score for six stereo headphones that were tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is ŷ = 22.458194 + 0.325418x, where x = price ($) and y = overall score. Brand Price ($) A B C D E F SSE=141.029 180 150 = 0.353 95 70 70 35 ✓ X Score X X 78 69 (a) Compute SST, SSR, and SSE. (Round your answers to three decimal places.) SST 1920 SSR 678.303 63 56 38 26 (b) Compute the coefficient of determination 2. (Round your answer to three decimal places.) ,2 = 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 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. o 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 large 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.) 0.594 X

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter4: Polynomial And Rational Functions

Section4.6: Rational Functions

Problem 11SC: Find the mean hourly cost when the cell phone described above is used for 240 minutes.

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Transcribed Image Text:The following data show the brand, price ($), and the overall score for six stereo headphones that were tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is ŷ = 22.458194 + 0.325418x, where x = price ($) and y = overall score. Brand A B с D E F Price ($) 180 150 95 70 70 35 Score X X X 78 69 63 56 38 (a) Compute SST, SSR, and SSE. (Round your answers to three decimal places.) SST = 1920 SSR = 678.303 SSE = 141.029 26 (b) Compute the coefficient of determination r². (Round your answer to three decimal places.) ₁² = = 0.353 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 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. o 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 large 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.) 0.594 X

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