Quiz Chapter 06.04: Nonlinear Models for Regression


(All Tests)


(More on Nonlinear Regression)


(More on Regression)

Pick the most appropriate answer

1. When using the transformed data model to find the constants of the regression model y = ae^{bx} to best fit \left( x_{1}, y_{1} \right), \, \left( x_{2}, y_{2} \right), \, ... \, , \, \left( x_{n}, y_{n} \right), the sum of the square of the residuals that is minimized is


2. 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 = ap^{b} is most nearly


3. The transformed data model for the stress-strain curve \sigma = K_{1} \varepsilon e^{-K_{2} \varepsilon} for concrete in compression, where \sigma is the stress and \sigma is the strain is


4. In nonlinear regression, finding the constants of the model requires solving simultaneous nonlinear equations. However in the exponential model y = ae^{bx} that is best fit to \left( x_{1}, y_{1} \right), \, \left( x_{2}, y_{2} \right), \, ... \, , \, \left( x_{n}, y_{n} \right), the value of b can be found as a solution of a nonlinear equation. That equation is given by


5. There is a functional relationship between the mass density \rho of air and the altitude h above the sea level

Altitude above sea level, h (km) 0.32 0.64 1.28 1.60
Mass Density, \rho, (kg/m3) 1.15 1.10 1.05 0.95

In the regression model \rho = k_{1} e^{k_{2}h}, the constant k_{2} is found as k_{2} = 0.1315. Assuming the mass density of air at the top of the atmosphere is 1/1000th of the mass density of air at sea level. The altitude in kilometers of the top of the atmosphere is most nearly


6. A steel cylinder at 80^{\circ}F of length 12" is placed in a commercially available liquid nitrogen bath at 315^{\circ}F. 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 (^{\circ}F) Thermal expansion coefficient (\mu in/in/^{\circ}F)
-320 2.76
-240 3.83
-160 4.72
-80 5.43
0 6.00
80 6.47

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