RecallWeave · course lab
Open the learnerFit a line.
Read what it misses.
Move the data, try your own line and inspect every residual. Least squares finds the smallest total squared vertical error for these rows.
Exact fractions · six fictional examples
Starting the lab…
1. Choose or edit the data
2–12 rows. Whole-number x and y from −20 to 20. Repeated rows count separately.
2. Try a line: ŷ = a + bx
Use a number or fraction such as 2/3. Up to three decimal places; magnitude at most 1000.
Copies exact coefficients into your trial.
See the vertical errors
Compare the exact result
- Fitted intercept a
- Fitted slope b
- Mean point (x̄, ȳ)
- Minimum SSE
- Trial SSE
- Trial's excess SSE
Calculated results will appear after valid input.
Every row, without rounding
Residual r = observed y − predicted ŷ. The table keeps both models visible.
| Point | x | y | Fit ŷ | Fit r | Fit r² | Trial ŷ | Trial r | Trial r² |
|---|
Correct the input to calculate a new table.
3. Evaluate the fitted line
Number or fraction from −40 to 40.
A line evaluation is not a prediction interval. Even an in-range value is not guaranteed accurate.
Why this is a minimum
Exact excess = mean-point term + slope term
Read the identity
The terms are nonnegative. This proves the minimum for equal-weight squared vertical errors. It does not establish linearity, causation or generalization to new data.
Try it · explain it · recall it
Take the sixteen-question course
Download the fixed lesson, then choose it under Bring your own lesson in the RecallWeave learner. The guide works all six examples and every transfer prompt.
Lab edits do not change these downloads. No automatic storage or uploads.
Preparing the embedded course and guide…