The following data show the brand, price ($), and the overall score for six stereo headphones that were tested by Consumer Reports (Consumer Reports website). The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is ŷ = 20.2301 + 0.3477x , where a = price ($) and y = overall score. Brand Price ($) Score Bose 170 76 Scullcandy 150 71 Koss 95 62 Phillips/O'Neill 70 56 Denon 60 40 JVC 55 25 a. Compute SST, SSR, and SSE (to 3 decimals). SST = SSR = SSE = b. Compute the coefficient of determination r2 (to 3 decimals). Comment on the goodness of fit. Hint: If r2 is greater than 0.70, the estimated regression equation provides a good fit. The least squares line Select your answer - Va good fit as Select your answer - v proportion of the variability in y has been explained by the least squares line. c. What is the value of the sample correlation coefficient (to 3 decimals)? Txy
The following data show the brand, price ($), and the overall score for six stereo headphones that were tested by Consumer Reports (Consumer Reports website). 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 = 20.2301 + 0.3477x , where a = price ($) and y = overall score. Brand Price ($) Score Bose 170 76 Scullcandy 150 71 Koss 95 62 Phillips/O'Neill 70 56 Denon 60 40 JVC 55 25 a. Compute SST, SSR, and SSE (to 3 decimals). SST = SSR = SSE = b. Compute the coefficient of determination r2 (to 3 decimals). Comment on the goodness of fit. Hint: If r2 is greater than 0.70, the estimated regression equation provides a good fit. The least squares line Select your answer - Va good fit as Select your answer - v proportion of the variability in y has been explained by the least squares line. c. What is the value of the sample correlation coefficient (to 3 decimals)? Txy
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Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Question
Transcribed Image Text:The following data show the brand, price ($), and the overall score for six stereo headphones that were tested by Consumer Reports (Consumer Reports
website). The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (Ilowest) to 100 (highest). The
estimated regression equation for these data is ŷ = 20.2301 + 0.3477x , where a
price ($) and y = overall score.
Brand
Price ($)
Score
Bose
170
76
Scullcandy
150
71
Koss
95
62
Phillips/O'Neill
70
56
Denon
60
40
JVC
55
25
a. Compute SST, SSR, and SSE (to 3 decimals).
SST =
SSR =
SSE =
%3D
b. Compute the coefficient of determination r (to 3 decimals).
%D
Comment on the goodness of fit. Hint: If r is greater than 0.70, the estimated regression equation provides a good fit.
The least squares line - Select your answer-
v a good fit as
Select your answer -
proportion of the variability in y has been explained by the least squares
line.
c. What is the value of the sample correlation coefficient (to 3 decimals)?
Txy =
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