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3-5 Modeling with Nonlinear Regression
Name: _______________________________
Exponential, Logarithmic, and Logistic Modeling

Regression can be used to model real-world data that exhibits exponential or logarithmic growth or
decay.
Example #1: Use the data in the table to determine a regression equation that best relates the gross
domestic product, GDP, (in billions of chained 2000 dollars) to the year. Estimate the 2020 GDP.
Year
GDP
1950
1960
1970
1980
1990
2000
1777.30 2501.80 3771.90 5161.70 7112.50 9817.00
Source: U.S. Dept. of Commerce
Step 1 Make a scatter plot.
a)
b)
c)
d)
Turn scatter plot on.
STAT EDIT
ENTER YEARS (as time since 1950 so 1950 is 0, 1960 is 10, and so on) in L1 and GPD in L2.
Adjust the window to fit the data.
Step 2 Find a function to model the data.


The graph appears to be rapidly rising.
We will try an exponential function.
QUESTION: Is the regression model a good fit for our data?
a) With the diagnostic feature turned on and we can use a correlation coefficient.
The closer the correlation coefficient r is to 1, the better fit the regression is for our data.
1) TURN THE DIAGNOSTIC ON.
2) Do this by using the catalog and scrolling down to diagnostic on. Hit ENTER so that is states
DONE.
b) STAT CALC: choose Exp Reg
c) TIME SAVER: to enter the equation in the y = for us, follow the steps
1) VARS
2) y-VARS
3) Function
4) y1
5) ENTER
If you skip step c you will have to manually type the equation into the y = .
Step 3 Estimate the 2020 GDP.
e) You may plug 70 into x by hand.
f) OR use the value option
1) 2nd TRACE
2) VALUE
3) Type 70 in for x
4) Hit ENTER
CHOOSING THE RIGHT REGRESSION
• a linear function
• a quadratic function
• a cubic function
• a quartic function
• a LN function
• an exponential function
• a power function
By looking at the scatter plot it may allow you to eliminate some of the regressions, but check your r value to
make the final decision.
Example #2: The spread of a given computer virus is measured over time.
Day
Machines
2
4
6
8
10
12
14
765
916
1004
1066
1115
1155
1188
What model will best describe its growth?
How many machines would be infected on day 9?
Example #3: The brightness of a point of light is measured at different distances.
Distance (m)
Brightness
(candelas)
20
30
40
50
60
70
80
18.36
8.16
4.59
2.94
2.04
1.50
1.15
a. What model will describe the data?
b. Calculate the regression model for the data
c. Estimate the brightness at 100 meters.