# Quiz Chapter 06.04: Nonlinear Models for Regression

 MULTIPLE CHOICE TEST NONLINEAR REGRESSION 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 $1/1000$th 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