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Linear Regression Calculator TI-84: How to Use

Updated · Standard formula, shown below

This page explains how to perform linear regression on a TI-84 graphing calculator and how to interpret the results. You enter your x and y data lists, run the LinReg function, and the calculator outputs the slope, intercept, and correlation coefficient. The steps below work for the TI-84 Plus, TI-84 Plus CE, and most other TI-84 models.

What Is Linear Regression on the TI-84?

Linear regression finds the straight line that best fits a set of paired data points. On the TI-84, this is done with the LinReg(ax+b) function, which calculates the least-squares line. The calculator returns the slope (a), the y-intercept (b), and—if you turn on diagnostics—the correlation coefficient (r) and coefficient of determination (r²). These values let you describe the relationship between two variables and make predictions.

For example, if you have data on hours studied and test scores, linear regression gives you an equation like score = 5.2 × hours + 40. You can then use that equation to estimate a score for any number of study hours.

How to Enter Data for Linear Regression

Before you run the regression, you must enter your data into lists. The TI-84 uses lists named L1, L2, L3, and so on. Here’s how to enter data:

  1. Press STAT and choose 1:Edit.
  2. If lists have old data, clear them: highlight the list name (e.g., L1), press CLEAR, then ENTER.
  3. Enter your x-values in L1 and your y-values in L2. Press ENTER after each value.
  4. Make sure each list has the same number of entries; otherwise, the calculator will give an error.

For example, to analyze the relationship between temperature (x) and ice cream sales (y), you might enter temperatures in L1 and sales in L2. The order matters—each pair must be in the same row.

Running the Linear Regression Calculation

Once your data is in the lists, follow these steps to run the regression:

  1. Press STAT, then use the right arrow to go to the CALC menu.
  2. Scroll down to 4:LinReg(ax+b) and press ENTER.
  3. Enter the lists you used. The default is L1 and L2, so if you used those, just press ENTER.
  4. If you used different lists, type e.g., 2nd L1 (which is 2nd 1), comma, 2nd L2 (2nd 2), then ENTER.
  5. Press ENTER again to see the results.

The screen will show the equation in the form y = ax + b, along with the values of a and b. If you have diagnostics turned on, you’ll also see r and r². If you don’t see r, you need to turn on diagnostics (see below).

Turning On Diagnostics to Get r and r²

Many users are confused when the TI-84 doesn’t show the correlation coefficient r. This happens when the “Diagnostic” mode is off. To turn it on:

  1. Press 2nd then CATALOG (the key labeled 0).
  2. Scroll down to DiagnosticOn and press ENTER twice.

After this, rerun the LinReg function. The r and r² values will appear. r tells you the strength and direction of the linear relationship (from -1 to 1). r² tells you how much of the variation in y is explained by x.

Using the Regression Equation for Predictions

Once you have the equation, you can predict y for a new x value. The easiest way is to use the calculator’s TABLE or VARS feature:

  1. After the regression, the equation is stored in Y1. Press Y= and confirm that Y1 contains the equation.
  2. To predict at a specific x, go to the home screen, press VARS, select Y-VARS, then 1:Function, then 1:Y1. Type the x value in parentheses, e.g., Y1(10), and press ENTER.
  3. The calculator will output the predicted y value.

For example, if your equation is y = 2.1x + 5 and you want y when x = 10, Y1(10) gives 26. This is a quick way to make predictions without manually calculating.

Common Mistakes and Troubleshooting

Here are frequent issues users run into and how to fix them:

  • Error: DIM MISMATCH – Your lists have different numbers of entries. Check L1 and L2 and make them equal.
  • No r or r² shown – Turn on diagnostics as described above.
  • Wrong lists used – If you used L3 and L4, you must specify them in the LinReg command. The default is L1 and L2.
  • Data not sorted – Sorting is not required for regression, but it helps when graphing the scatterplot.
  • Graph doesn’t show the line – After regression, press ZOOM and select 9:ZoomStat to see the data and the regression line.

Another common mistake is treating correlation as causation. A high r value means a strong linear relationship, but it doesn’t prove that x causes y.

Comparing TI-84 Models and Alternatives

The steps above work on all TI-84 Plus models (Silver Edition, CE, etc.). The TI-83 Plus has a similar process but uses LinReg(ax+b) in the same menu. If you don’t have a TI-84, many online calculators and spreadsheet programs (like Excel or Google Sheets) can do linear regression. For example, in Excel you can use the LINEST function or add a trendline to a chart. The TI-84 is popular in classrooms because it’s allowed on many exams, but for occasional use, a free online calculator may be quicker.

Frequently Asked Questions

How do I find the linear regression equation on a TI-84?

Enter your data into L1 and L2, then press STAT, go to CALC, choose 4:LinReg(ax+b), and press ENTER. The calculator will display the equation y = ax + b with the slope a and intercept b.

Why doesn’t my TI-84 show r and r²?

You need to turn on diagnostics. Press 2nd, then CATALOG (0), scroll to DiagnosticOn, and press ENTER twice. Then rerun the regression.

Can I do linear regression with more than two lists?

No, LinReg(ax+b) only uses two lists (x and y). For multiple regression, you would need a different tool, such as a computer program.

What if my data has a non-linear pattern?

Linear regression assumes a straight-line relationship. If your scatterplot shows a curve, consider other regression types like quadratic or exponential, which are also available in the CALC menu.

How do I graph the regression line on my TI-84?

After running LinReg, press Y= and make sure Y1 contains the equation. Then press ZOOM and select 9:ZoomStat to see the scatterplot and the line.

What is the difference between r and r²?

r is the correlation coefficient, measuring the strength and direction of the linear relationship (-1 to 1). r² is the coefficient of determination, which tells you the proportion of variance in y explained by x.

Related

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