Linear Regression
Least-squares fit for pasted x,y data, with standard errors, R² and a residual plot.
Data
x, y, and σy if you have it
One point per line, separated by a comma, tab, semicolon or space. A first line that is not numbers is taken as a header. Where a semicolon or tab is doing the separating, a comma is read as a decimal point.
Fit
Each point weighted by 1/σ², so the best-measured points pull hardest.
Rows that would not read
These lines are left out of the fit. Line numbers count every line of the box above, blank ones included.
Line of best fit
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Parameters
± one standard error
- Slope
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- Intercept
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- Pearson r
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- R²
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- Standard error of the estimate
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- Points fitted
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- Degrees of freedom
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- Reduced χ²
- —
Scatter about the line, in units of y
Weighted fits only
Data and fit
y vs x
The dashed line is the least-squares fit evaluated at each measured x.
Residuals
observed minus fitted, vs x
Scatter with no pattern is what a straight line should leave behind. A curve or a fan here says the model, not the noise, is what is off.