Being able to make predictions about the future based on evidence (data) from the past is an important skill in the worlds of business and science. Companies can plan how much they will budget for new equipment or emphoyees if they can see a steady growth in sales. Scientists can predict the results of experiments based on patterns they see in data. Linear relationships, data that seems to fall near a line, occur frequently in the real world. In this lesson, each student will graph the "best fit" line for a set of data and determine its equation.
graph paper
ruler
TI-83 calculator
Example: The total amount (in millions of dollars) spent by the government on mathematics research from 1985 through 1995 is shown in the table. Find the "best fit" line and write its equation. Predict the amount to be spent in 2000. To center your graph, let x = 0 correspond with 1985.
Year | 1985 | 1986 | 1987 | 1988 | 1989 | 1990 | 1991 | 1992 | 1993 | 1994 | 1995 |
Amount |
$91 |
$118 |
$128 |
$130 |
$151 |
$184 |
$185 |
$205 |
$212 |
$240 |
$245 |
The point for the average of the coordinates is (5, 171.72)
Another point on the line is (10,245)
slope = (245 - 171.72) / (10 - 5) = 14.7
equation is:
y - 245 = | 14.7(x - 10) |
y - 245 = | 14.7x - 147 |
y = | 14.7x + 98 |
Now you try these:
Week |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
Price |
350 |
360 |
365 |
325 |
395 |
400 |
330 |
335 |
365 |
390 |
375 |
350 |
390 |
400 |
425 |
#sold |
45 |
35 |
30 |
54 |
25 |
18 |
35 |
50 |
45 |
20 |
45 |
50 |
19 |
20 |
17 |
Age |
2 |
3 |
6 |
8 |
10 |
12 |
14 |
15 |
17 |
18 |
19 |
Height |
28 |
33 |
40 |
46 |
52 |
55 |
61 |
64 |
70 |
72 |
72 |