Skip to content
ENExplore Calculators

Residual Analysis Calculator

Work out residual analysis instantly with clear inputs, formula shown and shareable results.

About Residual Analysis Calculator

A residual is the observed value minus the fitted value. Their sum of squares drives the standard error of the estimate √(SSE/(n − 2)), and comparing SSE to the total sum of squares gives R².

Formulas

Residual

eᵏ = yᵏ − (a + b·xᵏ)

Standard error

s = √(SSE / (n − 2)), R² = 1 − SSE/SST

Worked example

With the default values below, Residual Analysis Calculator returns Sum of squared residuals of 2.40000000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Observed y values
2, 4, 5, 4, 5
Fitted slope
0.6
Fitted intercept
2.2
x values
1, 2, 3, 4, 5

Results

Sum of squared residuals
2.40000000
Standard error of the estimate
0.89442719
R²
0.60000000
Largest residual
1.000000

Step by step

  1. 1Values used
  2. 2Residual
  3. 3Standard error
  4. 4Sum of squared residuals= 2.40000000
  5. 5Standard error of the estimate= 0.89442719
  6. 6R²= 0.60000000
  7. 7Largest residual= 1.000000

Assumptions and limits

  • The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

For the fitted line y = 0.6x + 2.2?

The residuals are −0.8, 0.6, 1.0, −0.6 and −0.2, giving SSE = 2.4 against SST = 6, so R² = 0.6.

What should a residual plot look like?

Random scatter about zero. Any pattern or fanning indicates the model is misspecified.

Related Calculators

Residual Analysis Calculator | Calcrivo