4.1 Modeling Nonlinear Data


Create scatter plots of non linear data
Transform nonlinear data to use for
prediction

Exponential Function:

Power function:

To show exponential growth:
◦ We look for a common ratio
x
y
1
3
2
8.7
8.7/3=2.9
3
26.9
26.9/8.7=
3.09
4
82.6
82.6/26.9
=3.07
5
240
2.91
◦
ratio
Notice the common
ratio is about 3!

Linear- increases
by a constant
(slope)

Exponentialincreases by a ratio

The following table shows the heights of a
Pasfor tree after 5 months.
Graph age vs. height.
(L1 vs. L2)
Notice the graph shows
an exponential growth model
x
y
1
3
2
8.7
3
26.9
4
82.6
5
240
Remember, we can’t find
correlation or a regression line
unless the data is linear.
So how do we do this?
(L1) x
(L2) y
1
3
2
8.7
3
26.9
(L3)
log y
Take the logarithm of y.
4
82.6
In L3= log (L2)
5
240
Now graph (x,log y)= (L1, L3)
What do you notice?
The data is linear!!! So now we can use it to
predict!
If a variable grows exponentially, its logarithm grows linearally.
** this question will be a multiple choice on your test. For
example:
 The oil production per year shows an exponential increase in
productivity. How would you predict data using this model?





A) Graph the year versus oil production
B) Graph the logarithm of year versus oil production
C) Graph the year versus the logarithm of oil production
D) Graph the logarithm of year versus the logarithm of oil
production
E)We can’t predict data of exponential growth.
Answer: C) Graph the year versus the logarithm of oil production
The following data is a power function.
 When does a power law become linear?
Take the log x and log y in L3 and L4
Then graph L3, L4 :(log x, log y) L1 L2
L3
(Log
What do you
L1)
length
weight
notice?
1
2
1
2
It’s linear!!
2
17
2
17
3
53.1
4
129.2
5
248.7
3
53.1
4
129.2
5
248.7
L4
(log
L2)



What do we need to actually know from section
4.1?
If data grows exponentiallygraph (x, log y)
If data grows to a power functiongraph ( log x, log y)
That is it!!!! So don’t stress too much about this
section-if you know these 2 facts, you are good!