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Regression http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for the STEM undergraduate. Applications. Mousetrap Car. Torsional Stiffness of a Mousetrap Spring. Stress vs Strain in a Composite Material. A Bone Scan. Radiation intensity from Technitium-99m .

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Applications

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://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


The end

THE END

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


This rapper s name is

This rapper’s name is

  • Da Brat

  • Shawntae Harris

  • Ke$ha

  • Ashley Tisdale

  • Rebecca Black

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


The end1

THE END

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


The end2

THE END

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


Applications

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


Applications

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


Applications

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


Applications

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


Applications

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


Applications

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


Applications

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


The end3

THE END

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate


The average of the following numbers is

The average of the following numbers is

  • 4.0

  • 7.0

  • 7.5

  • 10.0

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate


The following data3

The following data

  • 27.480

  • 28.956

  • 32.625

  • 40.000

is regressed with least squares regression to y=a1x. The value of a1 most nearly is

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate


Applications

A scientist finds that regressing y vs x data given below to straight-line y=a0+a1xresults in the coefficient of determination, r2 for the straight-line model to be zero.

  • -2.444

  • 2.000

  • 6.889

  • 34.00

The missing value for y at x=17 most nearly is

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate


Applications

A scientist finds that regressing y vs x data given below to straight-line y=a0+a1xresults in the coefficient of determination, r2 for the straight-line model to be one.

  • -2.444

  • 2.000

  • 6.889

  • 34.00

The missing value for y at x=17 most nearly is

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate


Applications

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

  • -47.9

  • -47.4

  • 15.6

  • 28.2

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate


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