TI-83 Resource Website --Statistics -- Linear Regression

TI-83 Resource Website

Statistics

Linear Regression

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The TI-83 Calculator can find a line that best fits a given data point. This operation is called LINEAR REGRESSION. It is also referred to as LINE OF BEST FIT and METHOD OF LEAST SQUARES.

NOTE: This topics is the second part of a series of modules. Before continuing this module, please see Entering Data into Lists if you have not done so already. After completing this module, continue with the series by going to the next topic entitled Graphing a Regression Line.

Example: Find the line of best fit for the following data set:

X	Y
1	14
6	19
10	24
15	26

Step 1: The data should already be entered as lists in the calculator. Press STAT.

Step 2: Press right arrow button so that CALC is highlighted and the CALC menu appears (as shown). Use the blue down arrow to highlight 4:LinReg(ax+b).

Step 3: Press ENTER.

Step 4: Now enter the list names. Order matters! You must enter the list name for x (the independent variable) first, then the list name for y (the dependent variable).

For this example, the x values are stored in L1.

Notice above "1" on the number keypad is "L1" in yellow. Similarly, above "2" in yellow is "L2". Press the yellow 2ND button, then "1" on the keypad. L1 should appear on the screen.

Step 5: Type a comma after L1. The comma is located directly above the "7" on the number keypad.

Step 6: Enter L2 (this is the list where the y values are stored). Press the yellow 2ND button, then "2" on the keypad for L2.

Step 7: Press ENTER. The results will be shown on a new screen.

Interpreting the Results:

a:	slope of the line -- the coefficient of x
b:	the y-intercept -- the constant
r^2:	coefficient of determination
r:	linear correlation coefficient

For this example, the line of best fit for our given data would be y = 0.887x + 13.656, rounding the numbers to the nearest thousandths place. The last two numbers, r²and r, are used in statistics to determine how well the line matches to the data. You will learn more about these numbers in your statistics courses. NOTE: r² and r are NOT necessary for Linear Regression. If you do not see these numbers, see the module Diagnostic On in The Basics menu.

To Continue with this series, go to the next topic entitled Graphing a Regression Line

Related Links

Diagnostic On (under The Basics menu)

Entering Data into Lists

Inserting and Naming Lists

Scatterplots and STATPLOT

Graphing a Regression Line

This site was last updated 08/29/02 and is maintained by Donna L. Sperry

Step 2: Press right arrow button so that CALC is highlighted and the CALC menu appears (as shown). Use the blue down arrow to highlight 4:LinReg(ax+b).
Step 3: Press ENTER.

Step 4: Now enter the list names. Order matters! You must enter the list name for x (the independent variable) first, then the list name for y (the dependent variable). For this example, the x values are stored in L1. Notice above "1" on the number keypad is "L1" in yellow. Similarly, above "2" in yellow is "L2". Press the yellow 2ND button, then "1" on the keypad. L1 should appear on the screen.
Step 5: Type a comma after L1. The comma is located directly above the "7" on the number keypad.
Step 6: Enter L2 (this is the list where the y values are stored). Press the yellow 2ND button, then "2" on the keypad for L2.
Step 7: Press ENTER. The results will be shown on a new screen.