Simple linear regression
Ordinary least squares with a fitted intercept. RMSE uses n; residual standard error uses n − 2 and needs at least 3 pairs.
SIMPLE LINEAR REGRESSION / TRANSPARENT METHOD
Simple linear regression
One number per line in each box. Row 1 must refer to the same observation in both series. Empty cells are errors, never skipped.
This tab’s workspace
Interactive examples
Predefined synthetic data only. The link shares the example, never your numbers or metadata. Loading an example replaces current fields.
01Enter your data
Example⇧ Import or paste a table
Choose options explicitly. Missing cells are flagged, not skipped.
X and Y must describe the same rows. Selecting one column twice is allowed but yields a self-comparison, not independent evidence.
Review the table before importing
Uses the columns and decimal format selected above. Row numbers refer to the parsed table including the header; completely blank rows may already have been ignored. No correction or exclusion is automatic.
At most 80 notices are displayed; every row is checked.
The report retains the original table, edits and excluded rows. It contains data: share deliberately. This is an editable local trail, not a certification.
Compare table columns
Select up to 8 numeric columns. Every selected cell must be valid; no individual missing values are removed. This is a descriptive comparison, not a test between groups.
Resume an analysis from a file
Open a .json file exported by StatNivo. Replaces current data and recalculates in this calculator; nothing is uploaded.
Raw data: up to 10,000 values per series.
Temporary storage is off unless you select the option.
02Read your result
Loading the local calculator…
Export, save and share
Undefined values: empty cells. No additional rounding in CSV files. CSV headings use stable English identifiers for software compatibility.
Temporary storage is off unless you select the option. Optional sessionStorage, off by default. Keeps text, table and settings across tools and languages in this tab. Browser session restoration can retain it. Use “Delete saved data” on a shared device. Nothing is uploaded.
Paired observations
For readability the plot displays at most 1500 regularly selected rows; all rows are used in calculations and CSV. Coincident points may overlap.
Residuals against X
How we get the result
Inspect paired rows
50 rows per page. Original row positions are retained; CSV includes all observations.
UNDERSTAND, DON’T JUST CALCULATE
The method in practice
b = Sxy / Sxx; a = ȳ − b x̄; ŷ = a + b x; R² = 1 − SSE/SST
A line with known coefficients
For X = 1, 2, 3, 4 and Y = 3, 5, 7, 9, the fitted model is ŷ = 1 + 2x, with R² = 1. At X = 5 it predicts 11, outside the observed range: even a perfect fit does not validate extrapolation.
Practical checks before using a result
A constant series makes Pearson r undefined. A constant X also prevents a unique regression slope. With constant Y, R² is undefined.
Importing from Excel without shifting pairs
Paste the entire table, select its real delimiter and header, then preview it. In decimal-comma data, use a semicolon or tab as the column delimiter. If Y is missing in row 3, fix that row rather than moving row 4 up.
Practical checks before using a result
Sample or population?
For 2, 4, 4, 4, 5, 5, 7, 9 the population SD is 2; sample SD is √(32/7) ≈ 2.13809. Choose the population formula when describing the full population of interest, not because the number is smaller.
Standard deviation or standard error?
Standard deviation describes the spread of observations. The usual standard error of the mean is sample SD / √n under independent sampling with finite variance. For sample SD 10 and n = 25, SEM = 2. Repeated dependent readings do not automatically count as 25 independent measurements.
Importing from Excel without shifting pairs
Paste the entire table, select its real delimiter and header, then preview it. In decimal-comma data, use a semicolon or tab as the column delimiter. If Y is missing in row 3, fix that row rather than moving row 4 up.