Linear Regression Calculator Casio fx-991EX Guide

This guide explains how to perform linear regression on the Casio fx-991EX scientific calculator. You enter paired (x, y) data into the calculator’s Statistics mode, and it computes the slope, intercept, correlation coefficient, and predicted values. The fx-991EX is one of the most capable non-graphing calculators allowed in many exams, and its linear regression features are both powerful and easy to use once you know the menu steps.

What Is Linear Regression?

Linear regression finds the straight line that best fits a set of data points. The line is usually written as y = a + b·x (or y = mx + c, depending on your textbook). The calculator uses the least-squares method: it minimizes the sum of the squared vertical distances between the data points and the line. This gives you the slope (how much y changes per unit x) and the intercept (the value of y when x is zero). The correlation coefficient r tells you how strong the linear relationship is, from -1 to +1.

Entering Data on the fx-991EX

To start, turn on the calculator and press MENU, then select 2: Statistics. You’ll see a table with columns for x and y. For linear regression, choose 2: y = a + bx (the option may be labelled differently depending on firmware, but it’s the first linear option). Now enter each pair of values: type the x value, press =, type the y value, press =. Repeat for all data points. If you make a mistake, use the arrow keys to move to the cell and overwrite it.

For example, to enter the points (1,2), (2,4), (3,5), (4,7), you would input:

• 1 =, 2 =
• 2 =, 4 =
• 3 =, 5 =
• 4 =, 7 =

After entering all data, press AC to leave the table. The data is stored in memory.

Getting the Regression Results

Once your data is entered, press SHIFT then 1 (STAT) to open the statistics menu. You’ll see several submenus. Choose 5: Reg (regression). From there you can select:

• 1: a – the intercept
• 2: b – the slope
• 3: r – the correlation coefficient
• 4: x̂ – predicted x for a given y
• 5: ŷ – predicted y for a given x

For example, after entering the points above, you would get a ≈ 0.5, b ≈ 1.6, and r ≈ 0.98 (values rounded). The calculator also shows the sum of squares and other statistics under the Sum and Var submenus, but the regression outputs are the ones you need for a line of best fit.

Using the Regression for Predictions

To predict a y value from a new x, use the ŷ function. After you have the regression results, press SHIFT > 1 > 5: Reg > 5: ŷ. The calculator will ask for the x value. Type your x and press =. It returns the predicted y. Similarly, x̂ gives the predicted x for a given y. This is useful for interpolation (estimating within your data range) and extrapolation (estimating outside it, with caution).

Common Mistakes and Troubleshooting

Many users get errors because they forget to press AC after entering data, or they select the wrong regression type (e.g., quadratic instead of linear). Another common issue is entering data in the wrong columns – the x values must go in the first column and y in the second. If you see a Math Error, it usually means you tried to calculate a prediction without any data, or you divided by zero (e.g., all x values are the same). Also, check that your calculator is in the correct mode; if you’re in COMP mode, the STAT menu won’t appear.

If you need to clear all data, go to SHIFT > 1 > 4: Clear > 1: All. This is essential before entering a new dataset, otherwise the old data stays in memory.

Comparing the fx-991EX with Other Calculators

The fx-991EX is often compared with the TI-84 Plus CE and the Casio fx-991CW. The TI-84 has a full graphing screen and can show the scatterplot, but it’s more expensive and not allowed in some exams. The fx-991EX is faster for pure calculation, has a high-resolution display, and is permitted in most standardized tests (like the SAT, ACT, and AP exams). The newer fx-991CW has a similar interface but with a different menu layout; the regression steps are slightly different. If you’re used to the fx-991EX, the CW may feel unfamiliar, but both are capable.

Frequently Asked Questions

How do I find the correlation coefficient r on the fx-991EX?

After entering your data, press SHIFT > 1 > 5: Reg > 3: r. The value appears on the screen. It’s always between -1 and 1. A value close to 1 or -1 means a strong linear relationship, while 0 means no linear relationship.

Can I use the fx-991EX for multiple linear regression?

No, the fx-991EX only does simple linear regression with one independent variable. For multiple regression (e.g., y = a + b·x1 + c·x2), you need a graphing calculator or computer software. The fx-991EX does have quadratic and cubic regression, but not multivariate.

Why does my calculator give a different answer than Excel?

Excel’s LINEST function gives the same slope and intercept for the same data, but rounding differences can occur. The fx-991EX stores more decimal places internally, so if you round intermediate steps, your final answer may differ slightly. Always use the full precision of the calculator and only round at the end.

How do I clear the data memory?

Press SHIFT > 1 (STAT) > 4: Clear > 1: All. This erases all data and resets the statistics. If you only want to delete one point, navigate to it in the table and overwrite it, but clearing all is safer before a new dataset.

Is the fx-991EX allowed in exams?

Yes, the fx-991EX is permitted in most major exams, including the SAT, ACT, IB, and AP exams, as long as it’s in non-CAS mode (which it is by default). However, always check your specific exam board’s rules, as some local exams may have restrictions.

What does the ‘a’ and ‘b’ stand for in the regression output?

In the equation y = a + b·x, ‘a’ is the y-intercept (the value of y when x=0) and ‘b’ is the slope (the change in y for a one-unit change in x). Some textbooks use y = mx + c, where m is the slope and c is the intercept – it’s the same line, just different letters.

Related

• Free Coefficient of Variation Calculator
• Inverse Variation Equation Calculator: Formula & Examples
• Magnetic Variation Calculator: Find True Bearing

in x | x value | - | 5 | 0
in y | y value | - | 7 | 0
out slope | Slope (a) | - | 1.2 | 2
out intercept | Intercept (b) | - | 1 | 2
out corr | Correlation (r) | - | 0.98 | 2