Q1.
When
using the transformed data model to find the constants of the regression
model y=aebx 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 y=aebx that
is best fit to the
value of b can be found as a solution of a nonlinear equation.
That equation is given by
Q5. There
is a functional relationship between the mass density p
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,
(kg/m3) |
1.15 |
1.10 |
1.05 |
0.95 |
In the regression
model ,
the constant k2 is
found as
k2=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 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
|