Girl Guides is an international organization whose first Canadian troop was established in 1910. It has been going strong in Canada ever since. The table below shows the number of Girl Guides (in thousands) from 1989 to 1996. Find a cubic regression function to model the data.

Year
1989
1990
1991
1992
1993
1994
1995
1996
Number of girl scouts (thousands)
231
253.3
273.8
284.1
294.1
303.6
368.6
383.7

To simplify data involving years, typically one replaces Years with Years after Start Date. Using this standard, the table of values appears as follows.

Year after 1989
0
1
2
3
4
5
6
7
Number of girl scouts (thousands)
231
253.3
273.8
284.1
294.1
303.6
368.6
383.7

Step 1: Turn on the STAT PLOT; press 2nd, Y=, ENTER, ENTER.

Step 2: Clear the functions; press Y= then, CLEAR for each function that needs deleting.

Step 3: Select values for the viewing window; press WINDOW.

Step 4: Go to the lists; press STAT, ENTER.

Step 5: Clear the lists; press the up arrow until the column heading is highlighted then, CLEAR, ENTER.

Step 6: Enter the data.

Step 7: View the data; press GRAPH.

Step 8: Choose the regression model; press STAT, right arrow.

Step 9: Select the cubic regression; press 6.  If your display is different, click here for the display on the newer calculators.

Step 10: Place the cubic regression into the function area; press VARS, right arrow, ENTER, ENTER, ENTER.

Step 11: View the scatter plot and regression model; press GRAPH.

When writing the regression in standard form, often you need to round the values. How many places you round depends on how accurate the information must be.

The cubic regression model in standard form, rounded to two decimal places, is as follows:

y = 0.64x3 – 4.93x2 + 25.83 + 232.16