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
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd3b1f6cb-a985-48d9-bc23-d5653a1a3a5b%2F665a6e26-c3b5-47bc-aad1-b690ab56ec5c%2Fuchetrx_processed.png&w=3840&q=75)
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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