Holistic Numerical Methods

Transforming Numerical Methods Education for the STEM Undergraduate

 

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MULTIPLE CHOICE TEST

(All Tests)

NONLINEAR REGRESSION

(More on Regression Background)

REGRESSION

(More on Regression)

 

Pick the most appropriate answer.


Q1.  When using the transformed data model to find the constants of the regression model  to best fitthe sum of the square of the residuals that is minimized is

 


Q2. It is suspected from theoretical considerations that the rate of water flow from a firehouse is proportional to some power of the nozzle pressure.  Assume pressure data is more accurate.  You are transforming the data.

Flow rate, F (gallons/min)

96

129

135

145

168

235

Pressure, p (psi)

11

17

20

25

40

55

 The exponent of the power of the nozzle pressure in the regression model F=apb most nearly is

0.497

0.556

0.578

0.678

 


Q3. The transformed data model for the stress-strain curve for concrete in compression, where  is the stress and is the strain is

 


Q4.  In nonlinear regression, finding the constants of the model requires solving simultaneous nonlinear equations. However in the exponential model  that is best fit to the value of b can be found as a solution of a nonlinear equation. That equation is given by

 


Q5There is a functional relationship between the mass densityof air and the altitude above the sea level

Altitude above sea level,(km)

0.32

0.64

1.28

1.60

Mass Density,  (kg/m3)

1.15

1.10

1.05

0.95

In the regression model, the constant  is found as .  Assuming the mass density of air at the top of the atmosphere is  of the mass density of air at sea level.  The altitude in kilometers of the top of the atmosphere most nearly is

46.2

46.6

49.7

52.5

 


Q6.  A steel cylinder at 80oF of length 12" is placed in a commercially available liquid nitrogen bath -315oF  If the thermal expansion coefficient of steel behaves as a second order polynomial of temperature and the polynomial is found by regressing the data below,  

Temperature

(oF)

Thermal expansion

coefficient

(in/in/oF)

-320

2.76

-240

3.83

-160

4.72

-80

5.43

0

6.00

80

6.47

 the reduction in the length of the cylinder in inches most nearly is

0.0219

0.0231

0.0235

0.0307

 

 

 

Complete Solution

 

 

Multiple choice questions on other topics

 


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Copyrights: University of South Florida, 4202 E Fowler Ave, Tampa, FL 33620-5350. All Rights Reserved. Questions, suggestions or comments, contact kaw@eng.usf.edu  This material is based upon work supported by the National Science Foundation under Grant# Creative Commons License0126793, 0341468, 0717624,  0836981, 0836916, 0836805, 1322586.  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.  Other sponsors include Maple, MathCAD, USF, FAMU and MSOE.  Based on a work at http://mathforcollege.com/nm.  Holistic Numerical Methods licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.

 

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