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The accompanying data on y = normalized energy (J/m²) and x = intraocular pressure (mmHg) appeared in a scatterplot in the article "Evaluating the Risk of Eye Injuries: Intraocular Pressure During High Speed Projectile Impacts"+; an estimated regression function was superimposed on the plot. x 2761 19764 25713 3980 12782 19008 20782 19028 14397 9606 3905 25731 y 1553 14999 32813 1667 8741 16526 26770 16526 9868 6640 1220 30730 (a) Here is Minitab output from fitting the simple linear regression model. Predictor Constant Pressure Coef -5090 SE Coef 2257 1.2912 0.1347 3679.36 R-Sq 90.2% R-Sq (adj) 89.2% T -2.26 9.59 P 0.048 0.000 S Does the model appear to specify a useful relationship between the two variables? O Yes, since the R2 is small and the t-test P-value is large, this indicates a useful relationship between normalized energy and interocular pressure. O No, since the R² is large and the t-test P-value is small, this does not indicate a useful relationship between normalized energy and interocular pressure. O Yes, since the R² is large and the t-test P-value is small, this indicates a useful relationship between normalized energy and interocular pressure. O No, since the R² is small and the t-test P-value is large, this does not indicate a useful relationship between normalized energy and interocular pressure. O Yes, since the R² is small and the t-test P-value is small, this indicates a useful relationship between normalized energy and interocular pressure.

The accompanying data on y = normalized energy (J/m²) and x = intraocular pressure (mmHg) appeared in a scatterplot in the article "Evaluating the Risk of Eye Injuries: Intraocular Pressure During High Speed Projectile Impacts"+; an estimated regression function was superimposed on the plot. x 2761 19764 25713 3980 12782 19008 20782 19028 14397 9606 3905 25731 y 1553 14999 32813 1667 8741 16526 26770 16526 9868 6640 1220 30730 (a) Here is Minitab output from fitting the simple linear regression model. Predictor Constant Pressure Coef -5090 SE Coef 2257 1.2912 0.1347 3679.36 R-Sq 90.2% R-Sq (adj) 89.2% T -2.26 9.59 P 0.048 0.000 S Does the model appear to specify a useful relationship between the two variables? O Yes, since the R2 is small and the t-test P-value is large, this indicates a useful relationship between normalized energy and interocular pressure. O No, since the R² is large and the t-test P-value is small, this does not indicate a useful relationship between normalized energy and interocular pressure. O Yes, since the R² is large and the t-test P-value is small, this indicates a useful relationship between normalized energy and interocular pressure. O No, since the R² is small and the t-test P-value is large, this does not indicate a useful relationship between normalized energy and interocular pressure. O Yes, since the R² is small and the t-test P-value is small, this indicates a useful relationship between normalized energy and interocular pressure.

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 accompanying data on y = normalized energy (3/m²) and x = intraocular pressure (mmHg) appeared in a scatterplot in the article "Evaluating the Risk of Eye Injuries: Intraocular Pressure During High Speed Projectile Impacts"+; an estimated regression function was superimposed on the plot. 2761 19764 25713 3980 12782 19008 20782 19028 14397 9606 3905 25731 y 1553 14999 32813 1667 8741 16526 26770 16526 9868 6640 1220 30730 (a) Here is Minitab output from fitting the simple linear regression model. SE Coef Coef -5090 2257 0.1347 R-Sq (adj) - 89.2% Predictor Constant Pressure S3679.36 1.2912 90.2% T -2.26 0.048 9.59 0.000 P R-Sq Does the model appear to specify a useful relationship between the two variables? O Yes, since the R² is small and the t-test P-value is large, this indicates a useful relationship between normalized energy and interocular pressure. O No, since the R² is large and the t-test P-value is small, this does not indicate a useful relationship between normalized energy and interocular pressure. O Yes, since the R² is large and the t-test P-value is small, this indicates a useful relationship between normalized energy and interocular pressure. O No, since the R2 is small and the t-test P-value is large, this does not indicate a useful relationship between normalized energy and interocular pressure. O Yes, since the R² is small and the t-test P-value is small, this indicates a useful relationship between normalized energy and interocular pressure.
Transcribed Image Text:The accompanying data on y = normalized energy (3/m²) and x = intraocular pressure (mmHg) appeared in a scatterplot in the article "Evaluating the Risk of Eye Injuries: Intraocular Pressure During High Speed Projectile Impacts"+; an estimated regression function was superimposed on the plot. 2761 19764 25713 3980 12782 19008 20782 19028 14397 9606 3905 25731 y 1553 14999 32813 1667 8741 16526 26770 16526 9868 6640 1220 30730 (a) Here is Minitab output from fitting the simple linear regression model. SE Coef Coef -5090 2257 0.1347 R-Sq (adj) - 89.2% Predictor Constant Pressure S3679.36 1.2912 90.2% T -2.26 0.048 9.59 0.000 P R-Sq Does the model appear to specify a useful relationship between the two variables? O Yes, since the R² is small and the t-test P-value is large, this indicates a useful relationship between normalized energy and interocular pressure. O No, since the R² is large and the t-test P-value is small, this does not indicate a useful relationship between normalized energy and interocular pressure. O Yes, since the R² is large and the t-test P-value is small, this indicates a useful relationship between normalized energy and interocular pressure. O No, since the R2 is small and the t-test P-value is large, this does not indicate a useful relationship between normalized energy and interocular pressure. O Yes, since the R² is small and the t-test P-value is small, this indicates a useful relationship between normalized energy and interocular pressure.
(b) The standardized residuals resulting from fitting the simple linear regression model (in the same order as the observations) are 0.98, -1.57, 1.47, 0.50, -0.76, -0.84, 1.47, -0.85, -1.03, -0.20, 0.40, and 0.81. Construct a plot of e* versus x. [Note: The model fit in the cited article was not linear.] standardized residuals O 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 .. 5000 10000 15000 20000 25000 X standardized residuals 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 5000 10000 15000 20000 25000 X standardized residuals 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 Comment on the appearance of the plot. O The unusual curvature in the residual plot indicates that a straight-line model is appropriate for these two variables. O The linearity of the residual plot indicates that a straight-line model is appropriate for these two variables. O The linearity of the residual plot indicates that a straight-line model is not appropriate for these two variables. standardized residuals 1.5 1.0 0.5 : L 0.0 -0.5 -1.0 -1.5 5000 10000 15000 20000 25000 O The unusual curvature in the residual plot might indicate that a straight-line model is not appropriate for these two variables. O The lack of any obvious pattern in the residual plot might indicate that a straight-line model is not appropriate for these two variables. X O 5000 10000 15000 20000 25000 X
Transcribed Image Text:(b) The standardized residuals resulting from fitting the simple linear regression model (in the same order as the observations) are 0.98, -1.57, 1.47, 0.50, -0.76, -0.84, 1.47, -0.85, -1.03, -0.20, 0.40, and 0.81. Construct a plot of e* versus x. [Note: The model fit in the cited article was not linear.] standardized residuals O 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 .. 5000 10000 15000 20000 25000 X standardized residuals 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 5000 10000 15000 20000 25000 X standardized residuals 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 Comment on the appearance of the plot. O The unusual curvature in the residual plot indicates that a straight-line model is appropriate for these two variables. O The linearity of the residual plot indicates that a straight-line model is appropriate for these two variables. O The linearity of the residual plot indicates that a straight-line model is not appropriate for these two variables. standardized residuals 1.5 1.0 0.5 : L 0.0 -0.5 -1.0 -1.5 5000 10000 15000 20000 25000 O The unusual curvature in the residual plot might indicate that a straight-line model is not appropriate for these two variables. O The lack of any obvious pattern in the residual plot might indicate that a straight-line model is not appropriate for these two variables. X O 5000 10000 15000 20000 25000 X
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