How To Do Linear Regression On Ti-84

How to Do Linear Regression on a TI‑84 Calculator

Linear regression is a fundamental statistical tool that lets you find the best‑fit straight line through a set of data points. On the TI‑84 family of graphing calculators, the process is streamlined into a few button presses, making it easy for students and professionals alike to analyze relationships between variables. This guide walks you through every step—from entering your data to interpreting the output and drawing the regression line—so you can confidently perform linear regression on a TI‑84 Practical, not theoretical..

Getting Started: Preparing the Calculator

Before you begin, make sure your TI‑84 is in the correct mode for statistical work.

1. Turn on the calculator and press the STAT key.
2. Use the arrow keys to highlight EDIT and press ENTER. You will see the list editor with columns labeled L1, L2, … up to L6.
3. If any of these lists contain old data, clear them by moving the cursor to the list name (e.g., L1), pressing CLEAR, then ENTER. Repeat for each list you plan to use.

Now the calculator is ready to receive fresh data.

Entering Your Data

Linear regression requires two variables: an explanatory (independent) variable x and a response (dependent) variable y. Typically, you place x values in L1 and y values in L2 And that's really what it comes down to..

Step‑by‑Step Data Entry

1. With the cursor in L1, type the first x value and press ENTER. Continue down the column, entering each subsequent x value.
2. Move the cursor to the top of L2 (press ↑ until you highlight L2, then → to move into the column).
3. Enter the corresponding y values, pressing ENTER after each one.
4. Verify that each x in L1 lines up with its y in L2—the pairs should be in the same row.

Example: Suppose you have the following data representing hours studied (x) and test scores (y):

You would type 1, 2, 3, 4, 5 into L1 and 55, 65, 70, 80, 90 into L2.

Performing Linear Regression

Once the data are in place, the TI‑84 can compute the regression equation in seconds.

Using the Built‑In Stat‑Calc Menu

1. Press STAT, then arrow right to highlight CALC.
2. Scroll down to 4:LinReg(ax+b) (or 8:LinReg(a+bx) if you prefer the y‑intercept first; both give the same line). Press ENTER.
3. The calculator now asks for the lists containing your data. If you used L1 and L2, simply press ENTER again (the default is LinReg(ax+b) L1, L2).
4. If you stored your data in different lists, type them after the command, e.g., LinReg(ax+b) L3, L4, then press ENTER.

The screen will display several statistics:

• a – the slope of the line
• b – the y‑intercept
• r² – the coefficient of determination
• r – the correlation coefficient

Note: If you do not see r and r², you need to turn on diagnostics. Press 2ND → 0 (CATALOG), scroll to DiagnosticOn, press ENTER, then ENTER again to activate it. Return to the regression step and repeat Easy to understand, harder to ignore..

Interpreting the Output

Using the example data above, the calculator might return:

LinReg
y = ax + b
a = 8.5
b = 47
r² = 0.98
r = 0.99

• Slope (a = 8.5): For each additional hour studied, the predicted test score increases by 8.5 points.
• Intercept (b = 47): If a student studied zero hours, the model predicts a score of 47.
• Correlation (r = 0.99): Very strong positive linear relationship.
• Coefficient of Determination (r² = 0.98): About 98 % of the variability in test scores is explained by hours studied.

You can now write the regression equation as:

[ \hat{y} = 8.5x + 47 ]

where (\hat{y}) denotes the predicted test score.

Graphing the Regression Line

Visualizing the line alongside your scatter plot helps confirm that the fit is reasonable And that's really what it comes down to..

Creating a Scatter Plot

1. Press 2ND → Y= (STAT PLOT).
2. Choose Plot1 and press ENTER.
3. Highlight On and press ENTER.
4. Set Type to the first icon (scatter plot).
5. For Xlist, enter L1 (press 2ND → 1).
6. For Ylist, enter L2 (press 2ND → 2).
7. Choose a mark style (e.g., the small square) and press ENTER.

Displaying the Regression Equation on the Graph

1. Press Y= to access the function editor.
2. Clear any existing equations.
3. Press VARS, arrow right to Statistics, then arrow down to EQ, and select 1:RegEQ. Press ENTER. This pastes the regression equation (e.g., 8.5X+47) into Y1.
4. Press GRAPH. You should see the scatter points with the line of best fit drawn through them.

If the line does not appear, check that Plot1 is turned on and that the window settings accommodate your data. Adjust the window by pressing WINDOW and setting appropriate Xmin, Xmax, Ymin, and Ymax values, or simply press ZOOM → 9:ZoomStat to let the calculator set optimal bounds automatically Small thing, real impact..

Common Mistakes and How to Avoid Them

Even though the TI‑84 simplifies linear regression, a few pit