Regression

Regression

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM undergraduate http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

Applications



Mousetrap Car http://www.youtube.com/watch?v=XZ23q0QXPx0&t=1m25s http://numericalmethods.eng.usf.edu


Torsional Stiffness of a Mousetrap Spring

0.4

0.3

0.2

T

= k

0

+ k

1

θ

0.1

0.5

1

θ (radians)

1.5

2 http://numericalmethods.eng.usf.edu


Stress vs Strain in a Composite Material

3.0E+09

2.0E+09

1.0E+09

0.0E+00

0 0.005

0.01

Strain, ε (m/m)

0.015

σ

=

E

ε

0.02



A Bone Scan http://numericalmethods.eng.usf.edu


Radiation intensity from Technitium-99m http://numericalmethods.eng.usf.edu


Trunnion-Hub Assembly http://numericalmethods.eng.usf.edu


Thermal Expansion Coefficient Changes with Temperature?

-400 -300

7.00E-06

6.00E-06

5.00E-06

4.00E-06

3.00E-06

2.00E-06

-200

1.00E-06

-100

Temperature, o

F

0 100

α = a

0

+ a

1

T

+ a

2

T

2



Pre-Requisite Knowledge



Close to half of the scores in a test given to a class are above the

A. average score

B. median score

C. standard deviation

D. mean score http://numericalmethods.eng.usf.edu


Given y

1

, y

2

, ……….. y n deviation is defined as

, the standard

1.

.

i n ∑

=

1 y i

−

2

[ y

]

/ n

2.

.

3.

.

i n ∑

=

1

−

2

[ y y

] n i

/ i n ∑

=

1

[ y i

− y

]

2

/( n

−

1 )

4.

.

i n ∑

=

1

[ y

− y

]

2 i

/( n

−

1 ) http://numericalmethods.eng.usf.edu


Linear Regression



Given

( x

1

,y

1

), ( x minimization of

2

,y

2

), ……….. ( x n

, y n

), best fitting data to y=f ( x ) by least squares requires

A. ) i n

∑

=

1

[

y i

− f

( ) i

]

B. ) i n

∑

=

1 y i

− f

( ) i

C. )

D. ) i n ∑

=

1

[ y i

− f i n

∑

=

1

[ y i

− y

2 ]

,

( ) i

]

2 i n

∑

=

1 y

= n y i

0% 0% 0% 0%

) http://numericalmethods.eng.usf.edu

) )


)

The following data x y

1

1

20 30 40

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

1. -136

2. 400

3. 536

0% 0%

-136 400 http://numericalmethods.eng.usf.edu


0%

536


1

1

20 30 40


predicted value of y at x=20 is

1. -136

2. 400

3. 536

0% 0%



0%

536


1

1

20 30 40


residual of y at x=20 is

1. -136

2. 400

3. 536

0% 0%



0%

536

Nonlinear Regression



1.

2.

3.

4.

When transforming the data to find the constants of the regression model

1 1 2 2

( x n

,y n

), y=ae bx to best fit ( x ,y ), ( x ,y ),……….. the sum of the square of the residuals that is minimized is i n ∑

=

1

( y i

− ae bx i

2

) i n

∑

=

1 i n ∑

=

1

( ln(

( y y i i

−

)

− ln ln a a

−

− bx i bx i

)

2

)

2 i n

∑

=

1

( ln( y i

)

− ln a

− b ln( x i

)

)

2

0% 0% 0% 0% http://numericalmethods.eng.usf.edu


When transforming the data for stress-strain curve for concrete in compression, where

σ = k

1

ε e

σ is the stress and

ε

− k

2

ε is the strain, the model is rewritten as

A. ) ln

σ = ln k

1

+ ln

ε − k

2

ε

B. )

C. ) ln ln

σ

ε

σ

ε

= ln k

−

1 k

2

ε

= ln k

1

+ k

2

ε

D. ) ln

σ = ln( k

1

ε

)

− k

2

ε

0% 0% 0% 0%

) http://numericalmethods.eng.usf.edu

) )


)

Adequacy of Linear

Regression Models



The case where the coefficient of determination for regression of is one if n data pairs to a straight line

33% 33%

A. none of data points fall exactly on the straight line

33%

B. the slope of the straight line is zero

C. all the data points fall on the straight line

A.

B.


C.

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

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

A.

B.

C.


D.

The coefficient of determination varies between

A. -1 and 1

B. 0 and 1

C. -2 and 2

0% 0% d

1

0 an d

1


0%

-2 an d

2

The correlation coefficient varies between

A. -1 and 1

B. 0 and 1

C. -2 and 2

0% 0% d

1

0 an d

1


0%

-2 an d

2

If the coefficient of determination is 0.25, and the straight line regression model is y=2-0.81x, the correlation coefficient is

20% 20% 20% 20% 20%

A. -0.25

B. -0.50

C. 0.00

D. 0.25

E. 0.50

A.

B.

C.


D.

E.

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

20% 20% 20% 20% 20%

A. Very strong

B. Strong

C. Moderate

D. Weak

E. Very Weak

A.

B.

C.


D.

E.

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. 9

B. 19

C. 81

0% 0%

9



0%

81

The percentage of scaled residuals expected to be in the domain [-2,2] for an adequate regression model is

A. 85

B. 90

C. 95

D. 100

0% 0% 0%

90 95


0%

100

Regression

Regression

Applications

σ

ε

Pre-Requisite Knowledge

Linear Regression

∑

[

]

∑

∑

∑

Nonlinear Regression

∑

∑

Adequacy of Linear

Regression Models

Related documents

Products

Support

Regression

Regression

Applications

σ

ε

Pre-Requisite Knowledge

Linear Regression

∑

[

]

∑

∑

∑

Nonlinear Regression

∑

∑

Adequacy of Linear

Regression Models

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