MEEN 260
Introduction to Engineering Experimentation
Homework 5: Regression and Strain Gauges
Assigned:
Thursday, 14 Feb. 2008
Due:
Thursday, 21 Feb. 2008, 9:00am
Homework Problems:
Problem 1)
Consider the data set given below:
Measurement
x
y
1
0.1
5.5
2
0.3
7.4
3
0.6
9.1
4
1.2
16.4
5
1.5
22.1
6
1.6
24.4
7
1.7
26.9
8
1.9
32.8
Develop the least-squares fit to the following data using a linear regression
b
ax
y
+
=
, a
2
nd
order regression
2
1
y
ax
=
+
, and an exponential regression
ax
Ce
y
=
.
a)
Determine the coefficients for all three regression models based on the summation
formulas provided in the lecture notes. Derive your own summation formulas if
necessary.
Don’t
use built-in functions of Excel to get the regressions directly;
but you may use Excel to do the summations, generate the plots, etc.
b)
Determine the coefficients for all three regression models based on the matrix
formulation of regression as presented in the lecture notes.
You may use Matlab,
Maple or similar software to do the matrix inversion, but show the values for all
matrices and vectors in your homework.
c)
Do the coefficients obtained from both methods agree?
(If they don’t, you’ve
made a mistake)

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