MCD 4140 Computing for Engineers Self Study Exercise 7
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MCD 4140 Computing for Engineers
Self Study Exercise 7
Note: Tasks below can use for both hand calculation practice and programming practice.
Note: You might want to use extra sheet for hand calculation practice.
Task 1
Find the best fit line for the data given below by performing linear regression. Calculate the r2 value.
|
x |
y |
|
0.6 |
5.282 |
|
1.36 |
5 |
|
2.12 |
6.5 |
|
2.88 |
7.2656 |
|
3.64 |
7.2 |
|
4.4 |
8.588 |
|
5.16 |
10 |
|
5.92 |
11 |
Task 2
Find the best fit line for the data given below by performing non-linear regression using the Exponential Model. Calculate the r2 value. (Note: You can also try to solve this problem using Power Model and Saturation- Growth-Rate model)
|
X |
y |
|
0.6 |
5.282 |
|
3.64 |
7.2 |
|
6.68 |
10.5716 |
|
9.72 |
13.2164 |
|
12.76 |
17 |
|
15.8 |
22 |
|
18.84 |
29 |
Task 3
Use least-squares regression to fit a straight line to
|
x |
0 |
2 |
4 |
6 |
9 |
11 |
12 |
15 |
17 |
19 |
|
y |
5 |
6 |
7 |
6 |
9 |
8 |
7 |
10 |
12 |
12 |
Along with the slope and intercept, compute the standard error of the estimate and the correlation coefficient. Plot the data and the regression line. Then repeat the problem, but regress x versus y—that is, switch the variables. Interpret your results.
Task 4
You measure the voltage drop V across a resistor for a number of different values of current !. The results are
|
i |
0.25 |
0.75 |
1.25 |
1.5 |
2.0 |
|
v |
-0.45 |
-0.6 |
0.7 |
1.88 |
6.0 |
Use first- through fourth-order polynomial interpolation to estimate the voltage drop for ! = 1.15. Interpret your results.
Task 5
The specific volume of a superheated steam is listed in steam tables for various temperatures. For example, at a pressure of 3000 lb/in2, absolute:
|
T, °F |
700 |
720 |
740 |
760 |
780 |
|
v, fts/1hz |
0.0977 |
0.12184 |
0.14060 |
0.15509 |
0.16643 |
Determine v at T = 750 °F.
Task 6
The following data was gathered to determine the relationship between the pressure and the temperature of 1 kg of nitrogen with a fixed volume of 10 m3 .
|
T [K] |
253.15 |
273.15 |
293.15 |
313.15 |
323.15 |
343.15 |
373.15 |
393.15 |
|
p [N/m2] |
7500 |
8104 |
8700 |
9300 |
9620 |
10200 |
11200 |
11700 |
Employ the ideal gas law pV = nRT to estimate the constant R on the basis of this data. Note that the temperature T must be expressed in kelvins [K] (0°C = 273.15 K). The number of moles [mol] of nitrogen molecules (N2) is n = (1 kg) /(0.028 kg/mol). (The accepted value for R is 8.31447 N.m/(mol.K). Refer to website http://physics.nist.gov/cuu.)
Task 7
On average the surface area A of human beings is related to height H and weight W . Measurements on a number of individuals of height 1.80 m and different weights [kg-wt] give values of surface area [m2] in the following table.
|
W [kg-wt] |
70 |
75 |
77 |
80 |
82 |
84 |
87 |
90 |
|
A [m2] |
2.10 |
2.12 |
2.15 |
2.20 |
2.22 |
2.23 |
2.26 |
2.30 |
Show that a power law A = aWb fits these data reasonably well. Evaluate
the constants a and b , and predict what the surface area is for a person of height 1.80 m and weight 95 kg-wt.
Task 8
Fit a parabola to the data from table below. Determine the r2 for the fit and
comment on the efficacy of the result.
|
v, [m/s] |
10 |
20 |
30 |
40 |
50 |
60 |
70 |
80 |
|
F, [N] |
25 |
70 |
380 |
550 |
610 |
1220 |
830 |
1450 |
2023-01-13