1. Lesson 3

1.9. Explore 5

Mathematics 30-2 Module 4

Module 4: Polynomials

 

You need to be careful when modelling data using a regression. Sometimes the regression equation will tell you things that don’t make sense. Try This 3 explores this idea.

 

Try This 3

 

The number of births to women of a particular demographic in the United States is listed in the following table.

 

Year

Years Since 1970

Births (thousands)

1970

0

11.752

1980

10

10.169

1986

16

10.176

1990

20

11.657

1991

21

12.014

1992

22

12.220

1993

23

12.554

1994

24

12.901

1995

25

12.242

1996

26

11.146

1997

27

10.121

1998

28

9.462

1999

29

9.054

2000

30

8.519

2001

31

7.781

2002

32

7.315

2003

33

6.661
Source: Indiana University Southeast
  1.  
    1. Predict the shape of the scatter plot by looking at the data. Which regression model that you have learned so far would best model this data?
    2. Plot the data using a graphing calculator.
    3. Does the scatter plot cause you to change your mind about the type of regression that would best fit this data?
  2.  
    1. Use your calculator to determine a regression equation for the data. Make sure to round your values to four decimal places.
    2. Graph the regression equation on the same graph as your scatter plot. Does the graph of the equation appear to match the data?
  3.  
    1. Estimate the number of births in 1975.
    2. Estimate the number of births in 2010.
    3. Describe a problem with the prediction for 2010.
  4. Use the graph of your regression equation to predict a year when 3000 births will occur.

course folder Save your responses in your course folder.

You are trying to determine the x-value that will make 3 = −0.0014x3 + 0.064x2 − 0.6399x + 11.7298 true. Graphing the function y = 3 and finding where this crosses your regression equation will allow you to determine this answer.
The year 1975 is five years after 1970.
Your regression equation should be y = −0.0014x3 + 0.064x2 − 0.6399x + 11.7298.
If you are still unsure about the shape, try determining a linear, a quadratic, and a cubic regression to see which one matches the data best.
The independent variable is Years Since 1970, and it will go on the x-axis.