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Homework: Calculator Regression

Module by: Kenny M. Felder, Kenny M. Felder. E-mail the authors

Summary: This module provides sample problems which develop concepts related to using linear regression on a calculator to find the variation of data.

Exercise 1

Canadian Voters

The following table shows the percentage of Canadian voters who voted in the 1996 federal election.

Table 1
Age 20 30 40 50 60
% voted 59 86 87 91 94
  • a. Enter these points on your calculator lists.
  • b. Set the Window on your calculator so that the xx-values go from 0 to 60, and the yy-values go from 0 to 100. Then view a graph of the points on your calculator. Do they increase steadily (like a line), or increase slower and slower (like a log), or increase more and more quickly (like a parabola or an exponent)?
  • c. Use the STAT function on your calculator to find an appropriate function to model this data. Write that function below.
  • d. Graph the function on your calculator. Does it match the points well? Are any of the points “outliers?”

Exercise 2

Height and Weight

A group of students record their height (in inches) and weight (in pounds). The results are on the table below.

Table 2
Height 68 74 66 68 72 69 65 71 69 72 71 64 65
Weight 180 185 150 150 200 160 125 220 220 180 190 120 110
  • a. Enter these points on your calculator lists.
  • b. Set the Window on your calculator appropriately, and then view a graph of the points on your calculator. Do they increase steadily (like a line), or increase slower and slower (like a log), or increase more and more quickly (like a parabola or an exponent)?
  • c. Use the STAT function on your calculator to find an appropriate function to model this data. Write that function below.
  • d. Graph the function on your calculator. Does it match the points well? Are any of the points “outliers?”

Exercise 3

Gas Mileage

The table below shows the weight (in hundreds of pounds) and gas mileage (in miles per gallon) for a sample of domestic new cars.

Table 3
Weight 29 35 28 44 25 34 30 33 28 24
Mileage 31 27 29 25 31 29 28 28 28 33
  • a. Enter these points on your calculator lists.
  • b. Set the Window on your calculator appropriately, and then view a graph of the points on your calculator. Do they decrease steadily (like a line), or decrease slower and slower (like a log), or decrease more and more quickly (like a parabola or an exponent)?
  • c. Use the STAT function on your calculator to find an appropriate function to model this data. Write that function below.
  • d. Graph the function on your calculator. Does it match the points well? Are any of the points “outliers?”

Exercise 4

TV and GPA

A graduate student named Angela Hershberger at Indiana University-South Bend did a study to find the relationship between TV watching and Grade Point Average among high school students. Angela interviewed 50 high school students, turning each one into a data point, where the independent (xx) value was the number of hours of television watched per week, and the dependent (yy) value was the high school grade point average. (She also checked the types of television watched—eg news or sitcoms—and found that it made very little difference. Quantity, not quality, mattered.)

In a study that you can read all about at www.iusb.edu/~journal/2002/hershberger/hershberger.html, Angela found that her data could best be modeled by the linear function x=–0.0288x+3.4397x=–0.0288x+3.4397. Assuming that this line is a good fit for the data...

  • a. What does the number 3.4397 tell you? (Don’t tell me about lines and points: tell me about students, TV, and grades.)
  • b. What does the number –0.0288 tell you? (Same note.)

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