plotlineWPS · PHYSICS LAB
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CLASSROOM WORKSPACE / DEMO DATA

Add your measurements. See the fit. Try the slopes yourself.

LIVE FIT
Start with the calculated answer.

Position vs. time

10 measurements · uncertainties shown as ± ranges

FIG. 01
Scroll to zoom · drag to pan
2

Automatic results

BEST-FIT LINE · y = mx + b
Calculating…

Every included measurement has equal weight.

Slope m——
Intercept b——
R² / goodness of fit——
↗
Automatic slope limitsLines through every uncertainty box
Maximum—
Minimum—
Half-range Δm—
3

Try the slopes yourself

Start from the automatic lines, then move each one while keeping it through every uncertainty box. Your work stays separate from the calculated answers.

For students & teachers: what are we looking for?

Make the maximum slope as large as possible and the minimum slope as small as possible, while each line still crosses every included uncertainty box. For a downward line, the maximum is the less negative number. A line that crosses all boxes is compatible, but it may not yet be an extreme.

Discuss: Which boxes limit how far you can tilt? What happens to Δm when the measurement uncertainties grow? Use “Compare with automatic” to check your reasoning, and export a report to share your work.

Explore more · residuals, fit checks & predictions

Look a little closer

DIAGNOSTICS

What happens at x?

PREDICT
s→y = —

Use your fitted line to estimate a value.

BRING YOUR MEASUREMENTS

Import data

Paste cells from Excel or Google Sheets, or choose a file. You’ll map the columns before importing.

Up to 20,000 rows · files up to 10 MB

Graph settings

The band describes uncertainty in the fitted mean. It is separate from measurement errors and slope boundaries.

Axis limits
CLASSROOM QUICK GUIDE

Plot. Adjust. Explain.

01 / Bring your data

Type in the grid, paste a rectangular selection, or import CSV, TSV, XLSX or XLS. Columns can be in any order. Δx and Δy are optional, absolute ± uncertainties in your axis units; a blank means zero. Scientific notation such as 1.2e-3 works. Semicolon and tab imports accept decimal commas.

02 / Choose your fit

Ordinary least squares minimizes squared vertical residuals. Weighted fitting uses 1/Δy² and requires positive Δy for all included rows, interpreted as known one-standard-deviation uncertainties. Both treat x as exact for regression; Δx still appears on the graph and participates in slope boundaries. “Through origin” fixes b = 0.

Parameter ± values are one standard error. The 95% mean confidence band uses Student’s t for ordinary fits and a normal critical value for weighted fits with known uncertainties. It is not a prediction interval. R² is centered, including for origin fits, and may be negative; it is undefined for constant y.

03 / Understand slope boundaries

The maximum and minimum are the largest and smallest signed slopes of lines that intersect every included rectangle [x − Δx, x + Δx] × [y − Δy, y + Δy]. The origin restriction also applies if selected. This uses all your points, including their x uncertainties. For negative lines, “maximum” is the less negative slope.

Half-range Δm = (mmax − mmin)/2 is a geometric range, not a statistical standard error or confidence interval. It is centered on the boundary midpoint, which can differ from the best-fit slope. If no line is compatible, or slopes are unbounded, Plotline says so.

04 / Draw your own max and min

Choose “Adjust by hand” after viewing the automatic lines. Hover over a line to highlight it, then drag a round handle up or down to tilt it. Drag the body to shift it. Choose “My maximum” or “My minimum” if the lines overlap. Touch screens can drag the same handles; keyboard users can Tab to a handle and press ↑ or ↓. With “Through origin” selected, every adjustment pivots around (0, 0).

The box counter checks all included measurements, including Δx. Crossing every box means a line is compatible; it does not prove you found the extreme. Compare with the automatic answer when ready. Manual lines are saved with your project and included in graph and report exports while shown.

05 / Check and share

Residual = measured y − fitted y. Patterns can reveal a poor linear model; studentized residuals over 3 are suggestions to inspect, never automatic exclusions. Click a point to locate its row. Uncheck a row to exclude it. Export a crisp PNG, editable SVG, CSV with residuals, or a printable report. Save a project file to transfer the full experiment.

Shortcuts & privacy

⌘ / Ctrl Z Undo · ⇧ ⌘ / Ctrl Z Redo · ⌘ / Ctrl S Save project · ? This guide. Enter moves down the grid. Scroll over the plot to zoom; drag to pan; double-click to reset. Data is processed locally and saved in this browser. Device storage is not a backup; export a project for safekeeping.

Methods: NIST linear regression ↗ · NIST weighted least squares ↗

Start a new experiment?

Your current work can be recovered with Undo. Save a project file to keep a separate copy.