Linear Models…zing
Gauss
Lesson 1.5
Finite Differences
• The differences between each
y-value and the preceding one in
a table of values
• Basically tells if the line is good
for the model
• Example #1 on page 44
Leibniz
Residual
• Measure of the error
between the actual value
of the data, r, and the value
of y given by the model.
• Vertical distance between
actual point and model
point on a graph
• Example2 on page 46
Galois
Least Regression Lines
• For any set of data there is one
and only one line for which the
sum of the squares of the
residuals is as small as
possible.
• Linear Regression is the name
of the process
Calculator
• r  correlation coefficient
• The closer to 1 the better fit the
line. Close to zero is a poor fit
with perhaps no correlation
• r2  Coefficient of Determination
• A statistical measure that is the
proportion of variation between x and
y in a data set.
Example
• The lengths of the radii of the inscribed
circles in regular polygons whose sides
have length one unit are given
Number of
sides
Radius
3
4
5
6
7
0.289 0.500 0.688 0.866 1.038
8
9
1.207
1.374
1. Draw a scatter plot
2. Calculate the finite differences for the data points
3. Find the model that best fits the data using the regression
feature on the calculator
4. What does the correlation coefficient indicate about the
data?
I think that is it!
• Get to work you little
whippersnappers!
Newton