ELEC 471

Prof. Rich Kozick

## ** Class Example: Least-Squares Fit of Line Slope
**

Suppose that X and Y are two variables that can be approximately
described by the linear function *Y = a X*
for some value of the constant *a*.
Your job is to determine or "estimate" the value of *a*
from the following five pairs of measurements of (X, Y):
X Y
--- ---
1.00 0.688
1.78 0.849
3.16 2.152
5.62 3.024
10.00 5.453

A MATLAB program `lsline.m`
is linked to this assignment on the Web.
The MATLAB program plots the data values, and it also allows
you to plot the "fit" provided by the equation *Y = a X*
for values of the parameter *a* that you set in the program.
What do you think is the "best" estimate of the parameter
*a* to fit the given data with the relation *Y = a X*?
Justify your answer as *quantitatively* as you can.
Explain exactly how you arrived at your choice of *a*.
Note that there is not a single correct answer, but there
are many incorrect answers!