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Section 3.5
Modeling with Nonlinear Regression
Exponential Regression
• Enter your data in L1 and L2
o L1 = independent variable
o L2 = dependent variable
• Create a scatterplot
o Determine if it resembles growth or decay
• Use ExpReg
o STAT button, CALC tab
• Copy this regression equation in Y=
o
o
o
o
Press “Y=“, Press “VARS”
Choose “5. Statistics”
Choose “EQ”
Choose “RegEQ”
Example 1
A. BACTERIA The growth of a culture of bacteria is
shown in the table. Use exponential regression to
model the data. Then use your model to predict how
many bacteria there will be after 24 hours.
Example 1
B. NATURE The number of leaves falling per hour from
the trees in an arboretum is shown in the table below.
Use an exponential regression model to predict how
many leaves will fall in the tenth hour.
Logarithmic Regression
• Enter your data in L1 and L2
o L1 = independent variable
o L2 = dependent variable
• Create a scatterplot
o Determine if it resembles growth or decay
• Use LnReg
o STAT button, CALC tab
• Copy this regression equation in Y=
o
o
o
o
Press “Y=“, Press “VARS”
Choose “5. Statistics”
Choose “EQ”
Choose “RegEQ”
Example 2
A. MEMORY A group of students studied a photograph
for 30 seconds. Beginning 1 day later, a test was given
each day to test their memory of the photograph. The
average score for each day is shown in the table. Use
logarithmic regression to model the data. Then use
your model to predict the average test score after 2
weeks.
Example 2
B. Students do not remember everything presented to
them in a mathematics class. The table below shows
the average percentage of information retained t
days after the lesson by a group of students. Use a
logarithmic regression model to predict the students’
retention percentage on the tenth day.
Logistic Growth
Think about a bag of microwave
popcorn…draw a graph of the relationship
of the number of kernels of popcorn
popped as a function of time. Put time on
the x-axis, and # kernels popped on the yaxis.
Logistic Growth: when the amount of growth initially is exponential,
but slos down and levels out, approachign a horizontal asymptote.
Logistic Growth
Regression
• Enter your data in L1 and L2
o L1 = independent variable
o L2 = dependent variable
• Create a scatterplot
o Determine if it resembles growth or decay
• Use LogisticReg
o STAT button, CALC tab
• Copy this regression equation in Y=
o
o
o
o
Press “Y=“, Press “VARS”
Choose “5. Statistics”
Choose “EQ”
Choose “RegEQ”
Example 3
A. ADVERTISING The number of television ads for a
certain product affects the percentage of people who
purchase the product as shown in the table. Use
logistic regression to find a logistic growth function to
model the data. Then use your model to predict the
limit to the percentage of people who will purchase
the product.
Example 3
B. MUSIC The probability of a person liking a song
increases with the number of friends who say they also
like the song. The data shown in the table models this
situation. Use a logistic growth function to determine
the limit to the probability that a person will like a song
based on the number of friends who say they like the
song.