http://nm.mathforcollege.com regression. applications
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Regression
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Applications
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Mousetrap Car
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Torsional Stiffness of a Mousetrap Spring
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0.1
0.2
0.3
0.4
0.5 1 1.5 2
θ (radians)
To
rqu
e (
N-m
)
θkkT 10
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Stress vs Strain in a Composite Material
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0.0E+00
1.0E+09
2.0E+09
3.0E+09
0 0.005 0.01 0.015 0.02
Strain, ε (m/m)
Str
ess,
σ (
Pa)
E
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A Bone Scan
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Radiation intensity from Technitium-99m
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Trunnion-Hub Assembly
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Thermal Expansion Coefficient Changes with Temperature?
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1.00E-06
2.00E-06
3.00E-06
4.00E-06
5.00E-06
6.00E-06
7.00E-06
-400 -300 -200 -100 0 100 200
Temperature, oF
Th
erm
al e
xpan
sio
n c
oef
fici
ent,
α
(in
/in
/oF
)
2210 TaTaaα
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THE END
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Pre-Requisite Knowledge
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This rapper’s name is
A. Da Brat
B. Shawntae Harris
C. Ke$ha
D. Ashley Tisdale
E. Rebecca Black
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Close to half of the scores in a test given to a class are above the
A. B. C. D.
25% 25%25%25%A. average score
B. median score
C. standard deviation
D. mean score
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The average of the following numbers is
1. 2. 3. 4.
25% 25%25%25%2 4 10 14
1. 4.0
2. 7.0
3. 7.5
4. 10.0
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The average of 7 numbers is given 12.6. If 6 of the numbers are 5, 7, 9, 12, 17 and 10, the remaining number is
1. 2. 3. 4.
25% 25%25%25%
1. -47.92. -47.43. 15.64. 28.2
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Given y1, y2,……….. yn, the standard deviation is defined as
1. 2. 3. 4.
25% 25%25%25%
)1/(2
1
nyyn
ii
)1/(2
1
nyyn
ii
A. .
B. .
C. .
D. .
nyyn
ii /
2
1
nyyn
ii /
2
1
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THE END
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6.03Linear Regression
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Given (x1,y1), (x2,y2),……….. (xn,yn), best fitting data to y=f (x) by least squares requires minimization of
n
iii xfy
1
A. B. C. D.
25% 25%25%25%
n
iii xfy
1
2
1
n
iii xfy
n
yyyy
n
iin
ii
1
2
1
,
A.
B.
C.
D.
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The following data
1. 2. 3. 4.
25% 25%25%25%
x 1 20 30 40
y 1 400 800 1300
is regressed with least squares regression to y=a1x. The value of a1 most nearly is
A. 27.480
B. 28.956
C. 32.625
D. 40.000
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A scientist finds that regressing y vs x data given below to straight-line y=a0+a1x results in the coefficient of
determination, r2 for the straight-line model to be zero.
1. 2. 3. 4.
25% 25%25%25%
x 1 3 11 17
y 2 6 22 ?
The missing value for y at x=17 most nearly is
A. -2.444
B. 2.000
C. 6.889
D. 34.00
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A scientist finds that regressing y vs x data given below to
straight-line y=a0+a1x results in the coefficient of
determination, r2 for the straight-line model to be one.
1. 2. 3. 4.
25% 25%25%25%
x 1 3 11 17
y 2 6 22 ?
The missing value for y at x=17 most nearly is
A. -2.444
B. 2.000
C. 6.889
D. 34.00
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The following data
1. 2. 3.
33% 33%33%
x 1 20 30 40
y 1 400 800 1300
is regressed with least squares regression to a straight line to give y=-116+32.6x. The observed value of y at x=20 is
A. -136
B. 400
C. 536
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The following data
1. 2. 3.
33% 33%33%
x 1 20 30 40
y 1 400 800 1300
is regressed with least squares regression to a straight line to give y=-116+32.6x. The predicted value of y at x=20 is
A. -136
B. 400
C. 536
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The following data
1. 2. 3.
33% 33%33%
x 1 20 30 40
y 1 400 800 1300
is regressed with least squares regression to a straight line to give y=-116+32.6x. The residual of y at x=20 is
1. -136
2. 400
3. 536
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THE END
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6.04Nonlinear Regression
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When transforming the data to find the constants of the regression model y=aebx to best fit (x1,y1), (x2,y2),……….. (xn,yn), the sum of the square of the residuals that is minimized is
n
i
bxi
iaey1
2
1. 2. 3. 4.
25% 25%25%25%
n
iii bxay
1
2ln)ln(
n
iii bxay
1
2ln
n
iii xbay
1
2)ln(ln)ln(
A.
B.
C.
D.
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When transforming the data for stress-strain curve
21 lnlnln kk
A. B. C. D.
25% 25%25%25%
21lnln kk
21lnln kk
21 )ln(ln kk
21
kek for concrete in compression, where
is the stress andis the strain, the model is rewritten as
A.
B.
C.
D.
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6.05Adequacy of Linear Regression
Models
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The case where the coefficient of determination for regression of n data pairs to a straight line is one if
A. B. C.
33% 33%33%A. none of data points fall
exactly on the straight line
B. the slope of the straight line is zero
C. all the data points fall on the straight line
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The case where the coefficient of determination for regression of n data pairs to a general straight line is zero if the straight line model
A. B. C. D.
25% 25%25%25%A. has zero intercept
B. has zero slope
C. has negative slope
D. has equal value for intercept and the slope
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The coefficient of determination varies between
A. B. C.
33% 33%33%A. -1 and 1
B. 0 and 1
C. -2 and 2
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The correlation coefficient varies between
A. B. C.
33% 33%33%A. -1 and 1
B. 0 and 1
C. -2 and 2
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If the coefficient of determination is 0.25, and the straight line regression model is y=2-0.81x, the correlation coefficient is
A. B. C. D. E.
20% 20% 20%20%20%
A. -0.25
B. -0.50
C. 0.00
D. 0.25
E. 0.50
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If the coefficient of determination is 0.25, and the straight line regression model is y=2-0.81x, the strength of the correlation is
A. B. C. D. E.
20% 20% 20%20%20%
A. Very strong
B. Strong
C. Moderate
D. Weak
E. Very Weak
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If the coefficient of determination for a regression line is 0.81, then the percentage amount of the original uncertainty in the data explained by the regression model is
A. B. C.
33% 33%33%A. 9
B. 19
C. 81
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The percentage of scaled residuals expected to be in the domain [-2,2] for an adequate regression model is
A. B. C. D.
25% 25%25%25%A. 85
B. 90
C. 95
D. 100
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