Exponential And Logarithmic Functions And Models - Texas Instruments TI-84 Plus Manual

TI-83, TI-83 Plus, TI-84 Plus Guide
Use the tick marks to estimate rise divided by run and note a
possible y-intercept. After pressing
program, enter your guess for the slope and y-intercept.
After entering your guess for the y-intercept, your line is drawn
and the errors are shown as vertical line segments on the graph.
(You may have to wait a moment to see the vertical line
segments ) Press
.
Next, the sum of squared errors,
move the y-intercept of the line or change its slope to improve the fit to the data.
Press
ENTER
the
TRY AGAIN?
viewing the errors, enter another guess
for the y-intercept and/or slope. The
process of viewing your line, the errors,
and display of
If the new value displayed for
have improved the fit.
When you feel an
the minimum value is found, enter
the
TRY AGAIN?
program then overdraws the line of best
fit on the graph and shows the errors
for the line of best fit.
The program ends by displaying the coefficients a and b of the best-fit line y = ax + b as well as
the minimum
SSE
4
explore the method of least squares

1.3 Exponential and Logarithmic Functions and Models

As we begin to consider functions that are not linear, it is very important that you be able to
draw scatter plots, find numerical changes in output data, and recognize the underlying shape
of the basic functions to be able to identify which function best models a particular set of data.
Finding the model is only a means to an end − being able to use mathematics to describe the
changes that occur in real-world situations.
4
Program LSLINE is for illustration purposes only. Actually finding the line of best fit for a set of data should be done
according to the instructions in Section 1.4.2c of this Guide.
5
Two articles that further explain "best-fit" are H. Skala, "Will the Real Best Fit Curve Please Stand Up?" Classroom
Computer Capsule, The College Mathematics Journal, vol. 27, no. 3, May 1996 and Bradley Efron, "Computer-Intensive
Methods in Statistical Regression," SIAM Review, vol. 30, no. 3, September 1988.
Copyright © Houghton Mifflin Company. All rights reserved.
ENTER
to continue the program.
ENTER
, is displayed for your line. Decide whether you want to
SSE
and enter to choose
1
option. After again
is repeated.
SSE
is smaller than the value of
SSE
value close to
SSE
at
2
prompt. The
. Press
2ND MODE (QUIT)
5
that the calculator uses to find the line of best fit.
to resume the
for your first guess, you
SSE
to end the program Use program
.
to
LSLINE
27