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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

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

Mousetrap Car

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

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

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

A Bone Scan

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

Radiation intensity from Technitium-99m

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

Trunnion-Hub Assembly

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

Thermal Expansion Coefficient Changes with Temperature?

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

THE END

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

Pre-Requisite Knowledge

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

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

- average score
- median score
- standard deviation
- mean score

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

Given y1, y2,……….. yn,the standard deviation is defined as

- .
- .
- .
- .

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

THE END

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

Linear Regression

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

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

- -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 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 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 END

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

Nonlinear Regression

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

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

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

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

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

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

- -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

- -1 and 1
- 0 and 1
- -2 and 2

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

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

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

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

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

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for the STEM Undergraduate

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 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

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

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

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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