MasterTool

Linear Regression Calculator

Calculate linear regression using your data.

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What this tool does

Calculate linear regression using your data. Least-squares fit of a straight line. It describes association in the entered pairs — it does not establish that X causes Y, and it is sensitive to outliers.

How to use the Linear Regression Calculator

  1. Enter or select x values (comma or whitespace separated).
  2. Enter or select y values (same order as x).
  3. Enter or select predict y at x =.
  4. Read the calculated result; change any measurement to compare alternatives.

Formula

least squares: slope b = Σ(x−x̄)(y−ȳ)/Σ(x−x̄)²; intercept a = ȳ − b·x̄; R² = r²
x
X values (comma or whitespace separated)
y
Y values (same order as X)
x0
Predict Y at X =

Least-squares fit of a straight line. It describes association in the entered pairs — it does not establish that X causes Y, and it is sensitive to outliers.

Worked example

For linear regression calculator, the following measurements illustrate the exact method: X values (comma or whitespace separated): 1,2,3,4,5; Y values (same order as X): 2,4,5,4,5; Predict Y at X =: 6.

Inputs

  • X values (comma or whitespace separated)1,2,3,4,5
  • Y values (same order as X)2,4,5,4,5
  • Predict Y at X =6

Result

  • Slope (b)0.6
  • Intercept (a)2.2
  • Correlation (r)0.77
  • R²0.6
  • Predicted Y at the entered X5.8

Results explained

Slope (b)
Slope (b) from the formula above. Least-squares fit of a straight line. It describes association in the entered pairs — it does not establish that X causes Y, and it is sensitive to outliers.
Intercept (a)
Intercept (a) from the formula above. Least-squares fit of a straight line. It describes association in the entered pairs — it does not establish that X causes Y, and it is sensitive to outliers.
Correlation (r)
Correlation (r) from the formula above. Least-squares fit of a straight line. It describes association in the entered pairs — it does not establish that X causes Y, and it is sensitive to outliers.
R²
R² from the formula above. Least-squares fit of a straight line. It describes association in the entered pairs — it does not establish that X causes Y, and it is sensitive to outliers.
Predicted Y at the entered X
Predicted Y at the entered X from the formula above. Least-squares fit of a straight line. It describes association in the entered pairs — it does not establish that X causes Y, and it is sensitive to outliers.

Frequently asked questions

least squares: slope b = Σ(x−x̄)(y−ȳ)/Σ(x−x̄)²; intercept a = ȳ − b·x̄; R² = r²

Least-squares fit of a straight line. It describes association in the entered pairs — it does not establish that X causes Y, and it is sensitive to outliers.

Enter numbers only, in the units and format each label describes. Remove missing values rather than substituting zero, unless zero is a real observation.

No. Results describe the numbers you entered. Statistical inference also depends on sampling design, independence, model fit and interpretation; a p-value is not the probability that a hypothesis is true.

No. Every calculation, including the distribution algorithms, runs entirely in your browser.