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has been bonded to a steel beam, and is being calibrated. The resistance of the strain gauge is converted into a voltage appearing on a meter. Known forces (X, in kN) are applied, and voltmeter measurements (Y, in V) are as follows: 7 8 X 1 2 3 4 5 6 9 10 11 12 13 14 Y 4.4 4.9 6.4 7.3 8.8 10.3 | 11.7 || 13.2 || 14.8 || 15.3|| 16.5 17.2 18.9 19.3 (a) Fit a linear regression line Y = à +6X through the data and estimate the tension

has been bonded to a steel beam, and is being calibrated. The resistance of the strain gauge is converted into a voltage appearing on a meter. Known forces (X, in kN) are applied, and voltmeter measurements (Y, in V) are as follows: 7 8 X 1 2 3 4 5 6 9 10 11 12 13 14 Y 4.4 4.9 6.4 7.3 8.8 10.3 | 11.7 || 13.2 || 14.8 || 15.3|| 16.5 17.2 18.9 19.3 (a) Fit a linear regression line Y = à +6X through the data and estimate the tension

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
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Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Dont understand how to do c, d, e using matlab

A strain gauge is a device that measures elongation and is used to infer forces. A gauge has been bonded to a steel beam, and is being calibrated. The resistance of the strain gauge is converted into a voltage appearing on a meter. Known forces (X, in kN) are applied, and voltmeter measurements (Y, in V) are as follows: 5 6 7 8 9 10 X1 2 3 4 11 12 13 14 Y 4.4 4.9 6.4|| 7.3 8.8 || 10.3 | 11.7 | 13.2 | 14.8 || 15.3|| 16.5 || 17.2 || 18.9 | 19.3 (a) Fit a linear regression line Y = a +6X through the data and estimate the tension (force) in the beam when the meter reading is 13.8 V. Plot your results with the fitted line superimposed. Hint: Use polyfit for the fitting & polyval for the evaluation. (b) Estimate the residual standard deviation, Sg and find a 95% confidence interval for the regression slope. Is this slope statistically different from zero? What simplifica- tion can we make if it is? Hint: The 100(1-a)% confidence interval for the regression slope b is given by 6±ta/2,0-2 where Sg is the standard deviation of the residual errors, and Sx is the standard deviation of the 2-data. $²= ² (M-9) ² 72 $=(₁-2)²2²-(2)² i=1 SE Sx √n-2 i=1 point estimate (c) Test the hypothesis that the tension (force) in the beam is 10 kN when a voltmeter reading of 15 V is obtained. Hint: The point estimate is à + br, and the 100(1-a) % confidence interval for this is â+b/2-2 SE 1 + (x − x)²/S² n-2 uncertainty bounds (d) Plot the uncertainty bands for the point estimates on the plot. You should get 2 curves with a narrow waist that like shown in above. (e) Sketch on the plot how the 2 uncertainty curves would look like if you increased a to 0.1. Confirm your results by re-running the analysis above.
Transcribed Image Text:A strain gauge is a device that measures elongation and is used to infer forces. A gauge has been bonded to a steel beam, and is being calibrated. The resistance of the strain gauge is converted into a voltage appearing on a meter. Known forces (X, in kN) are applied, and voltmeter measurements (Y, in V) are as follows: 5 6 7 8 9 10 X1 2 3 4 11 12 13 14 Y 4.4 4.9 6.4|| 7.3 8.8 || 10.3 | 11.7 | 13.2 | 14.8 || 15.3|| 16.5 || 17.2 || 18.9 | 19.3 (a) Fit a linear regression line Y = a +6X through the data and estimate the tension (force) in the beam when the meter reading is 13.8 V. Plot your results with the fitted line superimposed. Hint: Use polyfit for the fitting & polyval for the evaluation. (b) Estimate the residual standard deviation, Sg and find a 95% confidence interval for the regression slope. Is this slope statistically different from zero? What simplifica- tion can we make if it is? Hint: The 100(1-a)% confidence interval for the regression slope b is given by 6±ta/2,0-2 where Sg is the standard deviation of the residual errors, and Sx is the standard deviation of the 2-data. $²= ² (M-9) ² 72 $=(₁-2)²2²-(2)² i=1 SE Sx √n-2 i=1 point estimate (c) Test the hypothesis that the tension (force) in the beam is 10 kN when a voltmeter reading of 15 V is obtained. Hint: The point estimate is à + br, and the 100(1-a) % confidence interval for this is â+b/2-2 SE 1 + (x − x)²/S² n-2 uncertainty bounds (d) Plot the uncertainty bands for the point estimates on the plot. You should get 2 curves with a narrow waist that like shown in above. (e) Sketch on the plot how the 2 uncertainty curves would look like if you increased a to 0.1. Confirm your results by re-running the analysis above.
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