## A Deer Generation

An ecologist tracked and studied the deer in a local herd that were born early in 1987.

The table below shows the number of those deer still living at the beginning of the eight following years, represented by D.

 Year 1987 1988 1989 1990 1991 1992 1993 1994 1995 D 145 138 130 113 80 62 42 28 16

We will enter this data into a table on the calculator and look at the scatterplot that it generates.
1. First things first: press [2nd]-[STAT PLOT], and make sure that Plot 1 is on, that it is using L1 and L2 as the XList and YLIst respectively, and that you like the mark that will identify plotted points.

2. To enter the data onto lists, use the keystroke sequence:
[STAT] >> EDIT >> 1:Edit >> [ENTER]
This takes you to a screen that shows lists as columns, labeled L1, L2, L3.

3. If the list already has values showing, you can clear them out using this sequence:
[UP arrow until the label is highlighted] >> [CLEAR] >> [ENTER]

4. L1 is the default location for the independent variable (horizontal, or x- axis); we will use that to show the year.
When the list is empty, the cursor begins in the first position. The bottom line on the screen should show "L1(1)=". Key in "1987" and press [ENTER]. The "1987" will appear as the first item in L1. Put 1988 through 1993 in as values in L1.

5. L2 is the default location for the dependent variable (vertical, or y- axis); we will use that to show the deer population still living, D.
Enter the number of deer still living in L2. If you want to remove or add a number in a list use the [DEL]ete key or [2nd]-[INS]ert keys.

6. Can you determine an appropriate window to view all of the data points?
If you cannot, there is a built-in feature that automatically defines and opens a graph window that will show all data points in your lists:
[ZOOM] >> 9:ZoomStat >> [ENTER].

7. A regression equation is an equation that will generate a best fit graph, which will represent the data as closely as possible. Let's find the line of best fit for this data and see how it compares to our data points. To do this, use the sequence:
[STAT] >> [RIGHT arrow] >> 4:LinReg (ax+b) >> [ENTER] >> [ENTER] again.
You should get something that says "a =...", "b =...", "r2 =...", "r =...".
Briefly, the "r value" is a correlation coefficient; it tells how well the regression equation fits the data -- where a "0" is the worst fit, and the closer the absolute value is to "1", the better the fit.

8. We'd like to graph the regression equation along with the plotted points. The most efficient way to both calculate the regression equation and paste it in as a function ready to graph is to use the sequence:
[STAT] >> CALC >> 4:LinReg (ax+b) >> [2nd]-[L1] >> [,] >> [2nd]-[L2] >> [,] >> [VARS] >> Y-VARS >> 1:Function >> [ENTER] >> [specify Y1] >> [ENTER] >> [ENTER].

9. To see the graph, simply press [GRAPH]. First the data points appear, then the "Yn=" functions will appear in their numerical order.

10. How well does the line match with the data points?

11. What is the meaning of the slope and intercept here? That is, what do they tell us about the deer population?