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Regression Coefficient Calculator

Calculate the slope coefficient of a simple linear regression and test it.

About Regression Coefficient Calculator

The slope is the covariance divided by the variance of the predictor. Dividing it by its standard error gives a t statistic, and values beyond about two indicate a coefficient distinguishable from zero. A large coefficient with a large standard error tells you nothing, which is why the t statistic rather than the coefficient governs interpretation.

Formula

Regression Coefficient

β = covariance(x, y) ÷ variance(x); t = β ÷ standard error of β

β
Change in y for a one-unit change in x
t statistic
Coefficient divided by its standard error

Worked example

With the default values below, Regression Coefficient Calculator returns Regression Coefficient of 1.800000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Covariance of x and y
45
Variance of xminimum 0
25
Standard error of the slopeminimum 0
0.35
Sample sizeminimum 3
60

Results

Regression Coefficient
1.800000
T Statistic
5.14286
Degrees of Freedom
58
Lower Confidence Bound
1.11401
Significance
Highly significant

Step by step

  1. 1Values used
  2. 2Regression Coefficient
  3. 3Regression Coefficient= 1.800000
  4. 4T Statistic= 5.14286
  5. 5Degrees of Freedom= 58
  6. 6Lower Confidence Bound= 1.11401
  7. 7Significance= Highly significant

Assumptions and limits

  • The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Regression Coefficient calculated?

β = covariance(x, y) ÷ variance(x); t = β ÷ standard error of β The slope is the covariance divided by the variance of the predictor. Dividing it by its standard error gives a t statistic, and values beyond about two indicate a coefficient distinguishable from zero.

Why does Regression Coefficient matter?

A large coefficient with a large standard error tells you nothing, which is why the t statistic rather than the coefficient governs interpretation.

What values do I need to enter?

This calculator takes 4 inputs: Covariance of x and y, Variance of x, Standard error of the slope, Sample size. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.

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