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
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffb989860-4d1c-4fb5-9e6b-42a4528dce9c%2F465a2c75-9094-41d2-a302-c2f7a0a47f0a%2Fuo5r2br_processed.jpeg&w=3840&q=75)
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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