Modeling on the TI-83 and Ti-84
Math 111, Linear Regression Section 1.5
Definition: A mathematical model is a function that describes a situation in such a way that
predictions can be made when actual data is not available.
To find a regression equation on your calculator:
Go to STAT and choose EDIT, [ENTER].
Decide which information is input and which is output. Enter the
independent information in the L1 column and the dependent
information in the L2 column. Now, QUIT out of STAT.
Look at the data. You want to turn on a STAT PLOT.
Go to STAT PLOT, [2nd] [Y=], and choose the plot you want. For this
example, you choose Plot1, [ENTER]. Be sure the cursor is on the
word On, and [ENTER]. Then QUIT.
Go to [ZOOM]. You want to graph statistical data, so choose ZSTAT,
[9].
Note: the points are close to being in line, so a linear function would
be a good model.
Go back to [STAT] and use the right arrow to choose CALC.
Then choose the type of model you want. In this case, you want a
linear model, [4] since the data looks roughly linear. (Or move your
cursor to number 4 and [ENTER].)
[ENTER] again gives the slope b and the y-intercept a of the line that
“fits” the data.
r is the correlation coefficient. If –1 ≤ r ≤ –.95 or .95 ≤ r ≤ 1, the fit
is good.
To graph the regression equation, go to [Y=]. Then to get the
Regression Equation, [VARS], [5] for Statistics, then go over with
your right arrow to EQ and [ENTER]. Then [GRAPH].
Source: US Census Bureau, Statistical Abstract of the United States, 2001 Table 202, page 129
Per Capita Milk Beverage Consumption
t
M(t)
Years
Consumption
(Since 1980)
(gallons)
0
27.6
5
26.7
10
25.7
15
24.3
17
24.0
18
23.7
19
23.6
Source: http://www.shareholder.com/mcd/Charts.cfm
Revenue From Sales For McDonalds Restaurants
t
Years
(Since 1990)
1
2
3
4
5
6
7
8
9
10
11
12
S(t)
Franchised Sales
(millions of dollars)
12,959
14,474
15,756
17,146
19,123
19,969
20,863
22,330
23,830
24,463
24,838
25,692
Annual Earnings of The Estée Lauder Companies
t
E(t)
Years
Earnings
(Since 1998)
(millions of dollars)
0
236.8
1
272.9
2
314.1
3
347.7
4
289.4