When to use regression on SAT math: use it when a question gives you data (a table or a list of points) and asks for the equation, a missing constant, a prediction, or whether the pattern is linear or exponential. Type the data into a Desmos table, add a regression, and read the numbers. R2 tells you how well the model fits. A value of 1 means a perfect fit.
Short answer: use regression only on data questions. If the question already gives you the equation, or the graph already shows the line, you do not need it. For more Desmos techniques, start at our Desmos SAT hub.
Learn this skill with Mr. O, free
Study the full Scatterplots and Statistical Claims lesson (free) Practice this skill (free)
Question banks: October 2026 Math question bank
Notes and practice need a free account: one click with Google, and you land straight on the lesson.
What is a regression on the SAT?
A regression finds the line or curve that best fits a set of points. The Desmos regressions guide puts it this way: a regression lets you "find a mathematical expression (like a line or a curve) to model the relationship between two sets of data."
Regression turns a data table into an equation. Take one free full-length adaptive section and use it on the clock.
Start 1-day free trial →The SAT tests this skill. College Board's Assessment Framework (version 4, September 2026) lists "Two-variable data: models and scatterplots" as an SAT Math skill. For the SAT it includes "Fit linear models to data represented in a scatterplot" and "Fit quadratic and exponential models to data represented in a scatterplot." The same domain asks students to "fit models to data and compare linear and exponential growth."
When to use regression on SAT math questions
Look at two things: what the question gives you, and what it asks for.
| The question gives you | It asks for | Use regression? |
|---|---|---|
| A table of x and y values | The equation of the function | Yes. Linear or exponential regression. |
| A table of values | Is it linear or exponential, increasing or decreasing? | Yes. Compare the fit of both models. |
| A model form with unknown letters, like y = a(b)x | The value of a or b | Yes. A custom regression with ~. |
| A scatterplot with the line of best fit already drawn | A predicted value | Usually no. Read it off the line. |
| The equation itself | A value of y for some x | No. Substitute. |
| Two points on a line | The slope or the equation | Either works. Regression gives slope and intercept in one step. |
Desmos is built into Bluebook for the entire Math section. For the official policy, read is Desmos allowed on the SAT.
How to run a regression on Desmos, step by step
These steps follow the Desmos regressions guide.
- Make a table. Type "table" on a new line, or add a table from the menu. Enter the x-values in x1 and the y-values in y1.
- Add the regression. Click Add Regression. Desmos says this "will automatically add a linear regression."
- Pick the model. Click Linear Regression to open the menu, and choose another model, such as exponential, if the data curves.
- Read the numbers. Desmos shows the values of the letters (like m and b) and a fit statistic: "correlation coefficient r (for linear regressions) or coefficient of determination R2 (for nonlinear regressions)."
- Or type your own model. Write the model with a tilde (~) instead of an equals sign, such as y1 ~ abx1. Desmos finds the best a and b.
One detail for the test: Desmos's College Board calculator guide (updated for the 2026-27 school year) says the test calculator "automatically checks Log mode when working with applicable exponential, logarithmic, and power regressions." Desmos's log mode article says that in log mode, "the r and r2 statistics are calculated according to the transformed data." So an exponential fit on the test reports its fit on the log scale.
Worked example 1: a linear table (October 2026 SAT)
From the October 2026 SAT Math Question Bank (Algebra, Linear Functions, rated Intermediate):
| x | y |
|---|---|
| −4 | 11 |
| 0 | 12 |
| 8 | 14 |
The table shows three values of x and their corresponding values of y. There is a linear relationship between x and y. Which of the following equations represents this relationship?
A) y = 1⁄4x + 12 B) y = 1⁄12x + 4 C) y = 4x + 12 D) y = 12x + 4
See which question types are costing you points
Start with a free mock, free drills, or preview sample questions before using all 45 question banks.
On Desmos: enter the table, add a linear regression (y1 ~ mx1 + b). The fit gives m = 0.25 and b = 12, with r = 1 because the points sit exactly on a line.
Show the answer
Answer: A) y = 1⁄4x + 12. The point (0, 12) gives the y-intercept, 12. From (0, 12) to (8, 14), y rises 2 while x rises 8, so the slope is 2/8 = 1/4. Check (−4, 11): 1/4 times −4 is −1, and −1 + 12 = 11. Choice C flips the slope.
Worked example 2: linear or exponential? (June 2026 SAT)
From the June 2026 SAT Math Question Bank (US) (Advanced Math, Exponential Growth and Functions, rated Easy):
For the function f, the table shows four values of x and their corresponding values of f(x).
| x | f(x) |
|---|---|
| 1 | 4,000 |
| 2 | 2,400 |
| 3 | 1,440 |
| 4 | 864 |
Which of the following could describe this function?
A) Decreasing exponential B) Increasing exponential C) Decreasing linear D) Increasing linear
On Desmos, try both models. We worked both least-squares fits, the method Desmos uses for every regression:
| Model | Fitted equation | Fit statistic |
|---|---|---|
| Linear, y1 ~ mx1 + b | y = −1,036.8x + 4,768 | r ≈ −0.976 (r2 ≈ 0.953) |
| Exponential, y1 ~ abx1 | y ≈ 6,666.67(0.6)x | R2 = 1 (exact fit) |
Show the answer
Answer: A) Decreasing exponential. Each value is 0.6 times the one before it: 2,400 ÷ 4,000 = 0.6, 1,440 ÷ 2,400 = 0.6, and 864 ÷ 1,440 = 0.6. A constant ratio means exponential. A ratio less than 1 means decreasing. The exponential model passes through every point, with b = 0.6.
An r of −0.976 looks strong, but it does not prove the data is linear. Compare the fit of each model. On a clean SAT table, pick the model whose fit is exactly 1.
What does r squared mean on Desmos?
R2, the coefficient of determination, is a score for how well the model fits the points. Desmos's article on negative R2 values explains it:
- "In most cases this value lies between 0 and 1 (inclusive)."
- "A common way to interpret R2 is as the fraction of variability in the dependent variable that the model accounts for." So 0 means the model explains none of the spread in y, and 1 means it explains all of it.
- It can even be negative: "R2 will be negative whenever your model's predictions are worse than a constant function that always predicts the mean of the data."
| What Desmos shows | What it means for an SAT table |
|---|---|
| r = 1 or −1 (linear) | The points sit exactly on a line. The sign matches the slope. |
| R2 = 1 (nonlinear) | The curve passes through every point. |
| Fit close to 1, but not 1 | Real data that scatters a little. Fine for a "line of best fit" question. |
| Fit far from 1, or negative | Wrong model. Try another one. |
r versus R2. r is the correlation coefficient. It runs from −1 to 1 and shows direction. Desmos notes that "apart from the special case of a linear regression model with an intercept term," R2 is "not actually equal to the square of any particular quantity." So for a line, R2 is r squared. For curves, it is its own score.
Does the SAT test r squared? The framework's list of SAT Math skills names fitting models, but it does not name r or R2. We searched the framework for "correlation" and found it only in research sections. Treat the fit statistic as your check, not as the answer.
What does RMSE mean in Desmos?
RMSE stands for root mean square error. It is the square root of the average squared error, where an error (a residual) is the vertical gap between a data point and the model. Smaller is better, and it is in the same units as y. For the linear fit in example 2, the residuals are about 268.8, −294.4, −217.6 and 243.2, so the RMSE is about 258. The exponential fit has an RMSE of 0.
The Desmos help articles we read describe r, R2 and residuals, which you can plot with one click. They do not describe an RMSE readout, so we cannot confirm where your version shows it. Either way, the reading is the same: closer to 0 means a better fit.
When should you not use regression?
- The line is already drawn. In College Board's own sample question about a line of best fit, the answer explanation just reads the graph: "At x = 32, the line of best fit has a y-value between 2 and 3."
- The equation is given. Substitute the value. No data, no regression.
- The ratio is obvious. If each y is a clean multiple of the last, you can see "exponential" without the calculator, as in example 2.
More cases like these are in when not to use Desmos on SAT math. For tables that are a clean ratio, the faster tool is in ratios and percentages on Desmos. To find where two models cross, use the method in how to solve for x on Desmos.
Where to practice regression questions
- Worked practice. SAT regression practice problems on Desmos, solved, and SAT exponential functions on Desmos from a table.
- Free lesson notes. The Growth Factors and Linear vs Exponential Models lesson notes and the Reading Data lesson notes teach one skill at a time. A free account is needed to open them.
- Bank questions. Both examples come from our October 2026 and June 2026 Math banks. Every bank is on our SAT question bank page.
- Timed practice. Create a free account to take one full-length adaptive SAT section free. You get a real Module 1 to Module 2 route and a scaled score. You can also browse all Digital SAT practice tests.
How we built this page
Desmos steps and the meaning of r and R2 come from the Desmos Help Center (Regressions, Log Mode, Nonlinear Regressions, and "Why am I seeing a negative R^2 value?") and Desmos's College Board calculator guide for 2026-27. SAT skill facts come from College Board's Assessment Framework for the Digital SAT Suite, version 4 (September 2026). The two example questions come from The Test Advantage's October 2026 (database test 4235, question 758151) and June 2026 US (test 3145, question 618740) SAT Math banks; we read each keyed answer in our database and solved it again by hand, and both matched. The regression numbers in example 2 are our own least-squares calculations. Verified 2026-10-13.
More guides on this skill
Frequently Asked Questions
When should you use regression on the SAT?
Use it when the question gives data, such as a table of x and y values or a list of points, and asks for an equation, a constant, a prediction or the type of growth. Skip it when the equation is given or the line of best fit is already drawn.
How do you do a regression on Desmos?
Put the data in a table, click Add Regression, and pick the model from the menu, such as linear or exponential. Or type the model with a tilde, like y1 ~ mx1 + b. Desmos shows the values of the letters and a fit statistic.
What does R squared mean on Desmos?
R squared, the coefficient of determination, shows how much of the spread in y the model explains. It is usually between 0 and 1. A value of 1 means the model passes through every point. Desmos shows r for linear regressions and R squared for nonlinear ones.
What does RMSE mean in Desmos?
RMSE is root mean square error: the square root of the average squared gap between each data point and the model. Smaller is better, and 0 means a perfect fit. The Desmos help articles we read describe r, R squared and residuals but do not describe an RMSE readout.
Does the SAT ask about r squared?
College Board's framework lists fitting linear, quadratic and exponential models to data as SAT skills, but it does not name r or R squared. Use the fit statistic to check your model choice.