Linear Regression Calculator
The straight line that fits a set of points best, with the equation, how much it explains, and a prediction.
Results
What this tool does
Least squares finds the one straight line that gets closest to every point at once — closest in the specific sense of making the squared vertical distances add up to the smallest possible total. Paste your x values and your y values, in the same order, and this page returns the equation, the share of the variation the line accounts for, and how uncertain the slope is. That last figure is the one most reports leave out, and it is the one that decides whether the trend you are about to describe is really there.
Formula
least squares: slope = Σ(x−x̄)(y−ȳ) ÷ Σ(x−x̄)² · the line passes through (x̄, ȳ)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
x_values | The x values, one per line or separated by commas | — |
y_values | The y values, in the same order | — |
predict_x | Predict y when x is | — |
OUT | The line of best fit | — |
SL | Slope | — |
IC | Where it crosses zero | — |
R2 | Of the variation the line explains | % |
RR | Correlation (Pearson r) | — |
PR | And y would be | — |
SE | Typical distance from the line | — |
SB | Uncertainty in the slope | — |
PV | p value (two-tailed) | — |
SG | The slope is more than noise | — |
DR | Direction | — |
CT | Count | — |
Worked example
- The x values, one per line or separated by commas1, 2, 3, 4, 5, 6, 7, 8, 9, 10
- The y values, in the same order2.1, 4.3, 5.9, 8.4, 9.8, 12.5, 14.1, 15.9, 18.6, 20.2
- Predict y when x is12
- The line of best fity = 2.0170 x + 0.0867
- Slope2.0170
- Where it crosses zero0.0867
- Of the variation the line explains99.81 %
- Correlation (Pearson r)0.9991
- And y would be24.2903
- Typical distance from the line0.2811
- Uncertainty in the slope0.0310
- p value (two-tailed)3.42015e-12
- The slope is more than noiseYes
- DirectionRising
- Count10
Limitations
- The calculation runs entirely in your browser. The values you type are never sent to a server.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
Frequently asked questions
What does the percentage explained actually mean?
It is how much of the up-and-down in your y values the straight line accounts for. At 100 per cent every point sits exactly on the line; at zero the line tells you nothing you would not get from the average of y. What it does not mean is that x causes y, or that the relationship is really a straight line — a perfect curve fitted with a straight line can still score above 90 per cent while being the wrong shape entirely. Plot the points before trusting the figure.
Can I predict outside the range of my data?
The arithmetic will happily give you a number, and that is the danger. A line fitted between x of one and ten says nothing about what happens at x of a hundred: nothing in your data speaks to that range, and real relationships bend, saturate or reverse. The prediction box here is most useful for filling a gap inside the range you measured. Outside it, the honest answer is that you are extrapolating and the line is an assumption, not a finding.