Complete the next two questions for the data given below. Put the data into your calculator and graph as a scatter plot.

Question

A study of the deer population in a certain forest yielded the following data.
 

Year	1964	1968	1972	1976	1980	1984	1988	1992
Deer	756	702	643	512	396	304	235	172

1) Find an equation of the line of regression for the deer study.

2) Describe the relationship of the scatterplot of the deer study. 

Answer 1

We first change the variable x into t such that t = x - 1964 and therefore t represents the number of years after 1964. Using t instead of x makes the numbers smaller and therefore managable. The table of values becomes.

We now use the table to calculate a and b included in the least regression line formula.

t	y	ty	t²
0	756	0	0
4	702	2808	16
8	643	5144	64
12	512	6144	144
16	396	6336	256
20	304	6080	400
24	235	5640	576
28	172	4816	784
∑t =112	∑y =3720	∑ty =36968	∑t² =2240

We now calculate a and b using the least square regression formulas for a and b.

a = (nΣt y - ΣtΣy) / (nΣt² - (Σt)²) = (8*36968 - 112*3720) / (8*2240 - 112²) = -22.5

b = (1/n)(Σy - a Σt) = (1/8)(3720 - (-22.5)*(112)) = 779.833

1)

Find the regression line.

y = at + b

   =- 22.5t+779.833

So regression line is - 22.5(x-1964)+779.833

Answer 2

2)

The given table

Year	Deer
1964	756
1968	702
1972	643
1976	512
1980	396
1984	304
1988	235
1992	172

From the table draw the scatterplot of the deer study.