Section 3 5 Modeling with Nonlinear Regression Exponential

Section 3. 5 Modeling with Nonlinear Regression

Exponential Regression • Enter your data in L 1 and L 2 o L 1 = independent variable o L 2 = dependent variable • Create a scatterplot o Determine if it resembles growth or decay • Use Exp. Reg o STAT button, CALC tab • Copy this regression equation in Y= o o Press “Y=“, Press “VARS” Choose “ 5. Statistics” Choose “EQ” Choose “Reg. EQ”

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 L 1 and L 2 o L 1 = independent variable o L 2 = dependent variable • Create a scatterplot o Determine if it resembles growth or decay • Use Ln. Reg o STAT button, CALC tab • Copy this regression equation in Y= o o Press “Y=“, Press “VARS” Choose “ 5. Statistics” Choose “EQ” Choose “Reg. EQ”

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 slows down and levels out, approaching a horizontal asymptote.

Logistic Growth Regression • Enter your data in L 1 and L 2 o L 1 = independent variable o L 2 = dependent variable • Create a scatterplot o Determine if it resembles growth or decay • Use Logistic. Reg o STAT button, CALC tab • Copy this regression equation in Y= o o Press “Y=“, Press “VARS” Choose “ 5. Statistics” Choose “EQ” Choose “Reg. EQ”

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.