15.8. Modeling with Regression http://www.ck12.org
y-intercept of 0.6191. Even though this number is not really in the relevant domain, it implies that as a newborn
baby Ben could kick the ball very slowly which is arguably true.
One weakness of the model is that it predicts that Ben will kick the ball at 0 miles per hour at age 68.1660. This
implies that Ben will not be able to kick the ball at all which isn’t necessarily true.
A second weakness of the model is that it predicts negative speed at either age extreme which doesn’t make sense.
A better model would be flat at 0 when Ben is born and also at the end of Ben’s life when he is no longer able to
kick the ball.
Practice
The table below shows the average height of an American female by age.
TABLE15.19:
Age (Years) Height (inches)
2 34
8 50
11 57
15 63
23 64
35 64- Determine two different equations that model the height over time using two different function families.
- Which function is a better fit for this data? Why?
- Use both equations to predict they-intercepts. What does they-intercept represent in each case? Are your
predictions reasonable for this part of the graph? - Use your “better fit” equation to predict the height of a 70 year-old woman. Is your prediction reasonable for this
part of the graph? Why or why not? What do you really need your model to do for the domain [16,100]?
Alice is in Wonderland and drinks a potion that approximately halves her height for each sip she takes, as shown in
the table below.
TABLE15.20:
# of sips Height (inches)
0 60
1 29
2 16
3 8
4 4.1- Do an exponential regression to determine an appropriate model. What is the equation?
- Explain why exponential regression is a good choice in this case.
- How many sips did she take if she is 2 inches tall?
- How tall will she be if she has 6 sips?
A rumor is spreading around your 400 person school. The following table shows the number of people who know
the rumor each day.