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The article "Vital Dimensions in Volume Perception: Can the Eye Fool the Stomach?" gave the following data on the dimensions of 27 representative food products (Gerber baby food, Cheez Whiz, Skippy Peanut Butter, and Ahmed's tandoori paste, to name a few). Product Maximum Width (cm) Minimum Width (cm) 1 2 2.50 2.90 2.70

The article "Vital Dimensions in Volume Perception: Can the Eye Fool the Stomach?" gave the following data on the dimensions of 27 representative food products (Gerber baby food, Cheez Whiz, Skippy Peanut Butter, and Ahmed's tandoori paste, to name a few). Product Maximum Width (cm) Minimum Width (cm) 1 2 2.50 2.90 2.70

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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The article "Vital Dimensions in Volume Perception: Can the Eye Fool the Stomach?"+ gave the following data on the dimensions of 27 representative food products (Gerber baby food, Cheez Whiz, Skippy Peanut Butter, and Ahmed's tandoori paste, to name a few). Product Maximum Width (cm) Minimum Width (cm) 1 2 O 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 Standardized Residual 3 2 2.50 1 2.90 2... 2.15 2 2.90 3.20 2.00 1.60 4.80 5.90 5.80 2.90 2.45 2.60 2.60 2.70 3.10 5.10 10.20 3.50 2.70 3.00 2.70 2.50 2.40 4.40 7.50 4.25 1.80 2.70 2.00 2.60 3.15 1.80 1.50 3.80 5.00 4.75 2.80 2.10 2.20 2.60 2.60 2.90 5.10 10.20 3.50 1.20 (a) Fit the simple linear regression model that would allow prediction of the maximum width of a food container based on its minimum width. (Round all numerical values to three decimal places.) 1.70 (b) Calculate the standardized residuals (or just the residuals if a computer program that doesn't give standardized residuals is used) and make a residual plot to determine whether there are any outliers. C 1.75 1.70 1.20 1.20 Residual LLL 2 2 10 12 Width 7.50 4.25 Minimum 0 6 8 10 12 12 Width Standardized 3 1 -1 Minimum Did deletion of this point result in a large change in the equation of the estimated regression line? O Yes, removing the point resulted in a reasonably substantial change in the equation of the estimated regression line. O Yes, removing the point did not result in a reasonably substantial change in the equation of the estimated regression line. O No, removing the point resulted in a reasonably substantial change in the equation of the estimated regression line. O No, removing the point did not result in a reasonably substantial change in the equation of the estimated regression line. O (d) For the regression line of part (c), interpret the estimated slope O For every 1-am increase in minimum width, the mean maximum width is estimated to decrease by the slope. O For every 1 increase in food products, the mean maximum width is estimated to increase by the slope. O For every 1-am increase in minimum width, the mean maximum width is estimated to increase by the slope. O For every 1 increase in food products, the mean maximum width is estimated to decrease by the slope. For the regression line of part (c), interpret the intercept. O The intercept would be an estimate of the mean maximum width when the minimum width is twenty-five. O The intercept would be an estimate of the mean maximum width when the minimum width is zero. O The intercept would be an estimate of the mean minimum width when the maximum width is zero. O The intercept would be an estimate of the mean minimum width when the maximum width is twenty-seven O The intercept would be an estimate of the mean maximum width when the minimum width is twenty-seven Standardized Residual 4 3 2 1 2 4 Minimum (c) The data point with the largest residual is for a 1-liter Coke bottle. Delete this data point and determine the equation of the regression line. (Round all numerical values to three decimal places.) 8 10 12 Width Ⓡ (e) For the data set with the Coke bottle deleted, are the assumptions of the simple linear regression model reasonable? Give statistical evidence. The pattern in the standardized residual plot suggests that the variances of the y distributions decrease as x increases, and therefore that the assumption of constant variance is not valid. O The pattern in the standardized residual plot suggests that the variances of the x distributions decrease as y increases, and therefore that the assumption of constant variance is valid. O The pattern in the standardized residual plot suggests that the variances of the x distributions decrease as y increases, and therefore that the assumption of constant variance is not valid. The pattern in the standardized residual plot suggests that the variances of the y distributions decrease as x increases, and therefore that the assumption of constant variance is valid. Standardized Residual 4. 2 1 0 2 4 6 8 10 Minimum 12 Width 0
Transcribed Image Text:The article "Vital Dimensions in Volume Perception: Can the Eye Fool the Stomach?"+ gave the following data on the dimensions of 27 representative food products (Gerber baby food, Cheez Whiz, Skippy Peanut Butter, and Ahmed's tandoori paste, to name a few). Product Maximum Width (cm) Minimum Width (cm) 1 2 O 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 Standardized Residual 3 2 2.50 1 2.90 2... 2.15 2 2.90 3.20 2.00 1.60 4.80 5.90 5.80 2.90 2.45 2.60 2.60 2.70 3.10 5.10 10.20 3.50 2.70 3.00 2.70 2.50 2.40 4.40 7.50 4.25 1.80 2.70 2.00 2.60 3.15 1.80 1.50 3.80 5.00 4.75 2.80 2.10 2.20 2.60 2.60 2.90 5.10 10.20 3.50 1.20 (a) Fit the simple linear regression model that would allow prediction of the maximum width of a food container based on its minimum width. (Round all numerical values to three decimal places.) 1.70 (b) Calculate the standardized residuals (or just the residuals if a computer program that doesn't give standardized residuals is used) and make a residual plot to determine whether there are any outliers. C 1.75 1.70 1.20 1.20 Residual LLL 2 2 10 12 Width 7.50 4.25 Minimum 0 6 8 10 12 12 Width Standardized 3 1 -1 Minimum Did deletion of this point result in a large change in the equation of the estimated regression line? O Yes, removing the point resulted in a reasonably substantial change in the equation of the estimated regression line. O Yes, removing the point did not result in a reasonably substantial change in the equation of the estimated regression line. O No, removing the point resulted in a reasonably substantial change in the equation of the estimated regression line. O No, removing the point did not result in a reasonably substantial change in the equation of the estimated regression line. O (d) For the regression line of part (c), interpret the estimated slope O For every 1-am increase in minimum width, the mean maximum width is estimated to decrease by the slope. O For every 1 increase in food products, the mean maximum width is estimated to increase by the slope. O For every 1-am increase in minimum width, the mean maximum width is estimated to increase by the slope. O For every 1 increase in food products, the mean maximum width is estimated to decrease by the slope. For the regression line of part (c), interpret the intercept. O The intercept would be an estimate of the mean maximum width when the minimum width is twenty-five. O The intercept would be an estimate of the mean maximum width when the minimum width is zero. O The intercept would be an estimate of the mean minimum width when the maximum width is zero. O The intercept would be an estimate of the mean minimum width when the maximum width is twenty-seven O The intercept would be an estimate of the mean maximum width when the minimum width is twenty-seven Standardized Residual 4 3 2 1 2 4 Minimum (c) The data point with the largest residual is for a 1-liter Coke bottle. Delete this data point and determine the equation of the regression line. (Round all numerical values to three decimal places.) 8 10 12 Width Ⓡ (e) For the data set with the Coke bottle deleted, are the assumptions of the simple linear regression model reasonable? Give statistical evidence. The pattern in the standardized residual plot suggests that the variances of the y distributions decrease as x increases, and therefore that the assumption of constant variance is not valid. O The pattern in the standardized residual plot suggests that the variances of the x distributions decrease as y increases, and therefore that the assumption of constant variance is valid. O The pattern in the standardized residual plot suggests that the variances of the x distributions decrease as y increases, and therefore that the assumption of constant variance is not valid. The pattern in the standardized residual plot suggests that the variances of the y distributions decrease as x increases, and therefore that the assumption of constant variance is valid. Standardized Residual 4. 2 1 0 2 4 6 8 10 Minimum 12 Width 0
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