11.5 Homework: calculator regression

Canadian voters

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

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 $x$ -values go from 0 to 60, and the $y$ -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?”

Height and weight

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

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?”

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.

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?”

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 ( $x$ ) value was the number of hours of television watched per week, and the dependent ( $y$ ) 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 $x=\mathrm{–0.0288}x+3.4397$ . 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.)