Linear Regression Calculator

1. Enter your x values, separated by commas.
2. Enter the matching y values, in the same order.
3. Read the best-fit line in the form y equals m x plus b.
4. See the slope and intercept, and how well the line fits.

Here is what each result means:

Linear regression finds the straight line that best fits a set of paired data points. The line is written as y equals m x plus b, where m is the slope and b the intercept. It is chosen by least squares, which means it makes the total of the squared vertical distances from the points to the line as small as possible.

That line lets you describe a trend and make predictions. Once you have the slope and intercept, you can estimate y for a new x, and the goodness of fit, r squared, tells you how much of the pattern the line captures. Regression is one of the most-used tools in statistics, science and business.

It uses the least-squares formulas to find the slope and intercept from your data.

1. Find the mean of the x values and of the y values.
2. Use the deviations from those means to compute the slope.
3. Get the intercept so the line passes through the point of means.

The slope here is the same idea as the slope between two points; the slope calculator handles that simpler case.

Fit a line to the points (1, 2), (2, 4), (3, 5), (4, 4), (5, 6).

Calculation: the mean of x is 3 and of y is 4.2. Working through the least-squares formulas gives a slope of about 0.8 and an intercept of about 1.8, so the best-fit line is roughly y = 0.8x + 1.8. The r squared is about 0.73, a good fit.

The two numbers describe the trend in plain terms.

The intercept is only meaningful when an x of zero makes sense for your data; otherwise treat it as a fitting constant.

The line and how well it fits are two different things.

A line always exists, but a low r squared warns that the points scatter far from it, so predictions will be rough.

The Spread of the Points

Tightly clustered points give a strong, reliable line; scattered points give a weak one.

Outliers

A single far-off point can pull the line toward it, changing the slope and intercept.

The Range of X

A wide range of x values gives a more stable slope than a narrow one.

Finding a Trend

Summarize how one variable moves with another as a single line.

Making Predictions

Estimate y for a new x from the fitted line.

Checking a Relationship

See from r squared whether a straight line is a reasonable model.

1. Fitting a Line to a Curve

If the data bends, a straight line misleads. Check a scatter plot first.

2. Ignoring Outliers

A single stray point can distort the line. Investigate before trusting the fit.

3. Predicting Far Outside the Data

The line is reliable only over the range you measured, not far beyond it.

4. Confusing Correlation with Cause

A strong fit shows association, not that x causes y.

5. Mismatched X and Y Counts

Each x needs a matching y. Unequal lists cannot be paired.

The least-squares formulas are exact; only the displayed decimals are rounded.

It is a method that fits the best straight line through paired data. The line, written y equals m x plus b, minimizes the total squared distance from the points, and it summarizes the trend between two variables.

Find the mean of x and y, then use the deviations from those means to compute the slope, and place the intercept so the line passes through the point of means. This tool does the full calculation.

R squared is the share of the variation in y that the line explains, from 0 to 1. An r squared of 0.8 means the line accounts for 80 percent of the pattern; the rest is scatter.

The slope is the trend, how much y changes per unit of x. R squared is how well the line fits. A steep slope can still have a low r squared if the points scatter widely.

Yes, within the range of your data. Plug a new x into the fitted line to estimate y. Predicting far outside the measured range is unreliable.

No. A strong fit shows the two variables move together, but correlation is not causation. Other factors, or chance, can explain the pattern.

At least two to define a line, but more points give a more reliable fit. A handful of well-spread points is far better than two.

A straight line will fit poorly, shown by a low r squared. Curved data needs a different model, such as a polynomial or an exponential fit.

No. The calculation runs in your browser and nothing you enter is stored or sent anywhere, unless you choose Save, which keeps the result only on this device.

• Linear regression (Wikipedia).
• Least squares regression (Maths Is Fun).
• Coefficient of determination (Wikipedia).