TI-84 Correlation Coefficient: How to Calculate r and r² Easily

Introduction

Calculating the correlation coefficient on a TI-84 calculator is an essential skill for statistics, AP Statistics, and data analysis. The calculator computes both r (the Pearson correlation coefficient) and r² (the coefficient of determination) from paired sample data. The value of r measures the strength and direction of a linear relationship, while r² tells you what percentage of variation in your dependent variable is explained by your regression line.

If you are practicing statistics without a physical calculator, you can follow every step directly in our free browser-based TI-84 Calculator Online.

What Is the TI-84 Correlation Coefficient?

The correlation coefficient (r) measures the strength and direction of a linear association between two quantitative variables. The value always ranges between -1.0 and +1.0:

What Is r² (Coefficient of Determination)?

The TI-84 also outputs r². This value represents the proportion of variance in the dependent variable (y) that is predictable from the independent variable (x).

For example, if r = 0.90, then r² = 0.81. This means 81% of the variation in the response variable is explained by the linear regression model, while the remaining 19% is due to unexplained factors or random variation.

Step-by-Step Instructions: Calculating r and r²

Step 1: Enter Your Data into Lists

1. Press [STAT] and select 1:Edit....
2. Enter your independent (x) data into column L1.
3. Enter your dependent (y) data into column L2.
4. Ensure both lists have the exact same number of entries.

Step 2: Turn On DiagnosticOn (Crucial Step)

By default, many TI-84 models have statistical diagnostics turned off, which hides r and r². You only need to enable this once:

1. Press [2ND] followed by [0] to open the [CATALOG].
2. Scroll down alphabetically to DiagnosticOn (or press the [D] key).
3. Press [ENTER], then press [ENTER] again until the screen displays Done.
4. Alternative (TI-84 Plus CE): Press [MODE], scroll down to STAT DIAGNOSTICS, and select ON.

Step 3: Run Linear Regression

1. Press [STAT] and arrow right to the CALC menu.
2. Choose 4:LinReg(ax+b) and press [ENTER].
3. Verify that Xlist is set to L1 and Ylist is set to L2.
4. Scroll down to Calculate and press [ENTER].

The calculator displays the slope (a), y-intercept (b), coefficient of determination (r²), and correlation coefficient (r).

Worked Example: Study Hours vs. Exam Score

Suppose you collect data comparing study hours (L1) to exam scores (L2):

After running LinReg(ax+b), the TI-84 displays:

• a = 4 (Score increases by 4 points per hour studied)
• b = 52 (Estimated baseline score with 0 study hours)
• r² = 1.0 (100% of score variation is explained by study hours)
• r = 1.0 (Perfect positive linear correlation)

Common Mistakes to Avoid

• Missing r and r² on Screen: Diagnostics are turned off. Enable DiagnosticOn from the Catalog.
• ERR: DIM MISMATCH: Column L1 and column L2 have unequal numbers of rows. Check your data entries.
• Swapping X and Y: Ensure the explanatory variable is in L1 and the response variable is in L2.
• Assuming Correlation Equals Causation: A high r value proves a strong mathematical association, but does not prove one variable causes the other.

Frequently Asked Questions

Why does my TI-84 show only a and b without r?

Press [MODE] > enable STAT DIAGNOSTICS: ON, or run DiagnosticOn from [2ND] + [0].

Can the correlation coefficient be greater than 1 or less than -1?

No. By definition, r is strictly bounded between -1.0 and +1.0. If a calculation yields a number outside this range, check your inputs for errors.

Summary

The TI-84 makes computing linear correlation and regression fast and straightforward. Remember to verify equal list lengths, keep DiagnosticOn enabled, and inspect a scatter plot to confirm linearity. Test this feature today on our online TI-84 calculator!