Statistics & data
Linearization & log plots
Transform data to test a linear model.
Your measurements
Number formats & units
Use decimal dots in datasets. Single values also accept decimal commas and scientific notation such as 1.2e-3 or 1.2 × 10⁻³.
Calculated locally. No account or uploads.
Result & working
ExampleThe calculator is loading. You can read the worked example below.
Download results
Excel and CSV files can be imported into Google Sheets.
More results
Show calculation steps
Interpretation & assumptions
Copy & export
Formula & example
The relationship
What the variables mean
| Symbol | Meaning |
|---|---|
| Transformed coordinates; regression is Y = mX + c. | |
| Reference | A positive reference quantity in the same unit as its input. It has no uncertainty in this model. |
| Residual | Observed transformed Y minus fitted Y. |
Worked example
- Data: x y, optionally followed by Δx Δy
- 1 3 0.01 0.1 2 12 0.01 0.2 3 27 0.01 0.3 4 48 0.01 0.4
- Transform x
- Square
- Transform y
- Unchanged
- X-axis label / unit
- x / s
- Y-axis label / unit
- y / m
Y = 3 X + 0
Follow the example steps
- Transform x using square; transform y using raw. Log references: x_ref = 1, y_ref = 1 in the corresponding input units.
- First row: (1, 3) → (1, 3). First-order uncertainties: ΔX = 0.02, ΔY = 0.1.
- Sxx = 129, Sxy = 387; m = Sxy/Sxx = 3.
- c = Ȳ − mX̄ = 22.5 − (3) × 7.5 = 0.
- Residuals are Y − (mX+c); SSE = 0. Y = 3 X + 0.
Common mistakes
Logarithms need a positive, dimensionless ratio.
Incorrect approach
ln(−2)
Correct approach
ln(2/1) ≈ 0.6931
More checks before you submit
- Do not take a logarithm of a non-positive value or a dimensioned quantity without a reference.
- Do not compare R² from different transformations as if they used the same residual scale.
- A high R² alone does not establish the physical model. Inspect residuals and uncertainty bars.
Method notes
Linearize the proposed equation before selecting axes. For T² = (4π²/g)L, plot T² vertically against L horizontally. For an inverse law, plotting y against 1/x can reveal a line. A log–log plot can estimate a power; a log–linear plot can estimate an exponential rate.
Logarithmic coordinates are drawn on equally spaced log-value axes, which corresponds to a logarithmic scale in the original quantity. Read labels as transformed values. Changing units or reference quantities changes a log intercept.
Uncertainties use local first-order derivatives. Large relative uncertainties give asymmetric transformed intervals and require more care. OLS here is unweighted and does not fit x errors; bars are displayed for inspection, not used as statistical weights.