Scatter Plot, Correlation, and Regression on the TI-83/84

See also:  a separate version of these instructions for the TI-89

Step 0. Setup

The calculator will remember these settings when you turn it off: next time you can start with Step 1.

Step 1. Make the Scatter Plot

Before you even run a regression, you should first plot the points and see whether they seem to lie along a straight line. If the distribution is obviously not a straight line, don’t do a linear regression. (Some other form of regression might still be appropriate, but that is outside the scope of this course.)

Step 2. Perform the Regression

Write down a (slope), b (y intercept), r (correlation coefficient). Round a and b to two more decimal places than your actual y values have; remember that final rounding should be done only at the end of calculations. Round r to two decimal places unless it’s very close to ±1 or to 0.
     a = −3.52
     b = 6.46
     r = −0.992

R² is the coefficient of determination. The closer it is to 1, the better a predictor is the regression equation. Another way to look at it is that in this case R² is about 98%, so 98% of the variation in y is associated with the variation in x.

Statisticians say that R² tells you how much of the variation in y is “explained” by variation in x, but if you use that word remember that it means a numerical association, not necessarily a cause-and-effect explanation.

Only linear regression will have a correlation coefficient r, but any type of regression will have a coefficient of determination R² that tells you how well the regression equation predicts y from the independent variable(s). (The calculator uses r², but most authors use R².)

See also:  What does R-squared mean?

Step 3. Display the Regression Line

Show line with original data points.

[GRAPH]

See also:  Once you have the regression line, you can use the calculator to predict the y value for any x in the model.

See also:  Do you wonder what sort of calculations the calculator does to find the best line? Least Squares, Down and Dirty explains what is meant by the “best” line and how to find it. Traditionally this is a calculus topic, but all that’s really necessary is some algebra.

See also:  The above procedure computes the linear correlation of the sample. Decision Points for Correlation Coefficient gives a simple test whether there is some correlation in the population, but you can also compute the actual correlation in the population.

Step 4 (optional). Display the Residuals

A plot of residuals can be helpful to show whether linear regression was the right choice.

If the residuals are more or less evenly distributed above and below the axis and show no particular trend, you were probably right to choose linear regression. But if there is a trend, you have probably forced a linear regression on non-linear data. If your data points looked like they fit a straight line but the residuals show a trend, it probably means that you took data along a small part of a curve.

The residuals are automatically calculated during the regression; all you have to do is plot them on the y axis against your existing x data.

Make the residuals visible in the statistics editor.	[STAT] [1] brings up the editor.   Cursor to the column heading of [L3] and press [2nd DEL makes INS] to open up a new list. You see the NAME= indicator at the bottom of the screen, with the blinking A to indicate alpha mode.   Press [2nd STAT makes LIST], then scroll to RESID and press [ENTER]. The list of residuals appears.
Turn off other plots.	Press [Y=]. Cursor to the highlighted = sign next to Y1 and press [ENTER]. Cursor to PLOT1 and press [ENTER].
Set up the plot of residuals against the x data.	Set up Plot 2 for the residuals. Press [2nd Y= makes STAT PLOT] [▼] [ENTER] [ENTER] to turn on Plot 2. Press [▼] [ENTER] to select a scatter plot.   The x’s are still in L1, so press [2nd 1 makes L1] [ENTER]. In this plot, the y’s will be the residuals: press [2nd STAT makes LIST], cursor to RESID, and press [ENTER] [ENTER].
Display the plot.	[ZOOM] [9] displays the plot.

Don’t worry about the magnitude of the residuals, because [ZOOM] [9] adjusts the vertical scale so that the points take up the full screen. What you want to look at is whether there’s a trend in the residuals. Here there is no trend, so you conclude that a linear regression was the right choice, as opposed to regression against some curve.

(By the way, if you want to remove the residuals list from your statistics editor, just cursor to the column heading and press [DEL].)