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Regression 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. Torsional Stiffness of a Mousetrap Spring. Stress vs Strain in a Composite Material.

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slide1
Regressionhttp://numericalmethods.eng.usf.eduTransforming Numerical Methods Education for the STEM undergraduate

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

applications
Applications

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

mousetrap car
Mousetrap Car

http://www.youtube.com/watch?v=XZ23q0QXPx0&t=1m25s

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

torsional stiffness of a mousetrap spring
Torsional Stiffness of a Mousetrap Spring

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

stress vs strain in a composite material
Stress vs Strain in a Composite Material

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

a bone scan
A Bone Scan

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

radiation intensity from technitium 99m
Radiation intensity from Technitium-99m

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

trunnion hub assembly
Trunnion-Hub Assembly

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

thermal expansion coefficient changes with temperature
Thermal Expansion Coefficient Changes with Temperature?

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

pre requisite knowledge
Pre-Requisite Knowledge

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

close to half of the scores in a test given to a class are above the
Close to half of the scores in a test given to a class are above the
  • average score
  • median score
  • standard deviation
  • mean score

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

given y 1 y 2 y n the standard deviation is defined as
Given y1, y2,……….. yn,the standard deviation is defined as
  • .
  • .
  • .
  • .

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

linear regression
Linear Regression

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

given x 1 y 1 x 2 y 2 x n y n best fitting data to y f x by least squares requires minimization of
Given (x1,y1), (x2,y2),……….. (xn,yn), best fitting data to y=f (x) by least squares requires minimization of
  • )
  • )
  • )
  • )

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

the following data
The following data
  • -136
  • 400
  • 536

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

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

the following data1
The following data
  • -136
  • 400
  • 536

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

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

the following data2
The following data
  • -136
  • 400
  • 536

is regressed with least squares regression to a straight line to give y=-116+32.6x. The residual of y at x=20 is

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

nonlinear regression
Nonlinear Regression

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

slide19

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

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

when transforming the data for stress strain curve
When transforming the data for stress-strain curve

for concrete in compression, where

is the stress and

is the strain, the model is rewritten as

  • )
  • )
  • )
  • )

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

adequacy of linear regression models
Adequacy of Linear Regression Models

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

slide22
The case where the coefficient of determination for regression of n data pairs to a straight line is one if
  • none of data points fall exactly on the straight line
  • the slope of the straight line is zero
  • all the data points fall on the straight line

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

slide23

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

  • has zero intercept
  • has zero slope
  • has negative slope
  • has equal value for intercept and the slope

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

the coefficient of determination varies between
The coefficient of determination varies between
  • -1 and 1
  • 0 and 1
  • -2 and 2

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

the correlation coefficient varies between
The correlation coefficient varies between
  • -1 and 1
  • 0 and 1
  • -2 and 2

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

slide26
If the coefficient of determination is 0.25, and the straight line regression model is y=2-0.81x, the correlation coefficient is
  • -0.25
  • -0.50
  • 0.00
  • 0.25
  • 0.50

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

slide27
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
  • Very strong
  • Strong
  • Moderate
  • Weak
  • Very Weak

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

slide28

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

  • 9
  • 19
  • 81

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

slide29
The percentage of scaled residuals expected to be in the domain [-2,2] for an adequate regression model is
  • 85
  • 90
  • 95
  • 100

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate