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 MULTIPLE CHOICE TEST NONLINEAR REGRESSION REGRESSION

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 1.6 Mass Density,  (kg/m3) 1.15 1.1 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

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