Math
Slope of a line
Find slope and y-intercept from two points.
Calculators / Math / Least-squares line from summaries
Least-squares line from summaries calculator
Fit a straight line using centred summary statistics rather than a list of observations.
On this page
Slope2
Intercept1
Calculator controls
How to calculate
Fit a straight line using centred summary statistics rather than a list of observations.
Slope =
xy/xxIntercept =
my-xy/xx*mxWorked example
- Number of observations: 5
- Mean x: 3
- Mean y: 7
- Sum of squared x deviations: 10
- Sum of x-y deviation products: 20
- Slope: 2
- Intercept: 1
Assumptions and limits
Use paired observations from one sample. The sums are centred, not raw sums of squares; uncertainty, significance and goodness of fit are not estimated.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Fit a straight line using centred summary statistics rather than a list of observations. The fitted line is y = intercept + slope × x. The observation count documents the sample but does not alter these two coefficients once the centred sums and means are supplied.
When this tool is useful
The fitted line is y = intercept + slope × x. The observation count documents the sample but does not alter these two coefficients once the centred sums and means are supplied.
Understanding your inputs
| Input | Example |
|---|---|
Number of observations n | 5 |
Mean x mx | 3 |
Mean y my | 7 |
Sum of squared x deviations xx | 10 |
Sum of x-y deviation products xy | 20 |
Frequently asked questions
What does this model leave out?
Use paired observations from one sample. The sums are centred, not raw sums of squares; uncertainty, significance and goodness of fit are not estimated.
How do I reproduce the example?
Enter the displayed example values in their labelled units. Apply the formula before rounding; change one input at a time to compare scenarios.