Linear Regression on a Calculator: Step-by-Step

Updated 12 November 2026 · Standard formula, shown below

This guide walks you through solving a linear regression on a graphing calculator (like the TI-84 or TI-83) or a scientific calculator with statistical mode. You enter paired x and y data, and the calculator returns the slope, y-intercept, and correlation coefficient (r or r²) of the best-fit line. You’ll need your data organized in two lists and a calculator that supports linear regression (most graphing calculators do).

What You’ll Need

A graphing calculator (TI-83, TI-84, TI-Nspire, Casio fx-9750GII, or similar) or a scientific calculator with a stats mode (like the Casio fx-991EX).
Your data: two paired lists of numbers (x and y).
Basic familiarity with your calculator’s menu navigation (arrows, enter, etc.).

Step-by-Step

Clear old data (if any). Press STAT (or 2nd then DATA on some models), choose Edit (or ClrList), and clear any existing values in lists L1 and L2. This prevents leftover data from interfering.
Enter your x-values. In the list editor, cursor to the top of L1, type each x value, pressing ENTER after each. For example, if your x data is 1, 2, 3, type 1 ENTER, 2 ENTER, 3 ENTER.
Enter your y-values. Move to the top of L2 (use the right arrow key) and enter each corresponding y value, pressing ENTER after each. Make sure the pairs line up: the first y goes with the first x, and so on.
Open the regression menu. Press STAT, then use the right arrow to highlight CALC (or CALC on Casio).
Select Linear Regression. Scroll down to LinReg(ax+b) (or LinReg on Casio) and press ENTER. Some calculators ask for the lists; if so, enter L1, L2 (comma-separated) and press ENTER.
Calculate. The calculator will display the regression equation in the form y = ax + b (or y = a + bx depending on model). It also shows the correlation coefficient r and the coefficient of determination r² (if not shown, turn on diagnostics: press 2nd then 0 (CATALOG), scroll to DiagnosticOn, press ENTER twice, then redo the regression).
Write down the results. Note the values of a (slope), b (y-intercept), and r or r² (correlation). These are your linear regression outputs.
Optional: Graph the line. To see the line over your scatterplot, press Y=, enter the equation (e.g., 2.5X + 1), then press GRAPH. Make sure your window (ZOOM 9:ZoomStat) fits the data.

Common Mistakes

Mixing up lists: Entering x values into L2 and y into L1 will produce a regression of y on x that is actually backward—the slope will be for x as a function of y, not the intended relationship.
Forgetting to clear old data: Old values in L1 or L2 will be included in the regression, giving a wrong line.
Ignoring the correlation coefficient: A high r² doesn’t always mean the line is appropriate; check the scatterplot for curvature or outliers.
Misreading the equation form: Some calculators output y = a + bx instead of y = ax + b. Always note which variable is the slope.
Not turning on diagnostics: Without DiagnosticOn, the TI-84 may not show r and r², leaving you without a measure of fit.

Tips

Always plot the data first (scatterplot) to visually check for a linear trend before running regression.
Use the ZoomStat feature (ZOOM then 9) to automatically set a good window for your data.
If your calculator asks for Freq or Store RegEQ, leave them at defaults unless you need to store the equation.
For scientific calculators (like Casio fx-991EX), press MODE, choose STAT, then A+BX for linear regression, and enter data in the table that appears.
Round your final answer to a reasonable number of decimal places based on your data’s precision—usually 2-3 significant digits.

Troubleshooting

r and r² don’t appear: On TI calculators, press 2nd then 0 (CATALOG), scroll to DiagnosticOn, press ENTER twice, then repeat the regression.
Error: DIM MISMATCH: This means your lists have different lengths. Check that L1 and L2 have the same number of entries.
Error: SINGULAR MATRIX or INVALID DIM: This often happens if all x-values are identical (no variation). Linear regression requires at least two distinct x values.
Calculator shows a line but graph looks wrong: Your window may be off. Press ZOOM then 9 to set a window that fits your data.
Regression line doesn’t match data: Double-check that your data is entered correctly and that you selected the right regression type (LinReg, not QuadReg or ExpReg).

Frequently Asked Questions

Q: What does the slope (a) mean in linear regression?
A: The slope represents the change in y for a one-unit increase in x. For example, if a = 2, then y increases by 2 when x increases by 1.

Q: What is the difference between r and r²?
A: r is the correlation coefficient, ranging from -1 to 1, indicating the strength and direction of the linear relationship. r² (coefficient of determination) is the proportion of variance in y explained by x, ranging from 0 to 1.

Q: Can I do linear regression on a scientific calculator?
A: Yes, many scientific calculators (like the Casio fx-991EX) have a STAT mode that supports linear regression. You enter data in a table and then access the regression results via the SHIFT + STAT menu.

Q: How do I predict a y value from a new x using the regression equation?
A: Once you have the equation y = ax + b, simply substitute the new x value into the equation. For example, if y = 2.5x + 1 and x = 10, then y = 2.5(10) + 1 = 26.

Q: Why does my calculator show a different equation form (y = a + bx)?
A: Some calculators (like Casio) use the form y = a + bx, where b is the slope and a is the y-intercept. This is mathematically equivalent to y = bx + a, but you need to know which variable is which to interpret correctly.

Q: What if my data has outliers?
A: Outliers can heavily influence the regression line. It’s wise to plot the data and consider removing or investigating extreme points that don’t follow the overall pattern, but only if you have a valid reason.

Method: the standard formula for this calculation, rounded as each result states. See how the calculators work or report an error.