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Simple Linear Regression Calculator

Variable Names (optional):
Explanatory (x) Response (y)
Data goes here (enter numbers in columns):
Include Regression Line:
Include Regression Inference:
Null Hypothesis:$H_0: \beta=0$
Alternative Hypothesis:$H_a: \beta$ $0$
Significance level: $\alpha=$


  • Values of the response variable $y$ vary according to a normal distribution with standard deviation $\sigma$ for any value of the explanatory variable $x$. The quantity $\sigma$ is an unknown parameter.

  • Repeated values of $y$ are independent of one another.

  • The relationship between the mean response of $y$ (denoted as $\mu_y$) and explanatory variable $x$ is a straight line given by $\mu_y=\alpha+\beta x$ where $\alpha$ and $\beta$ are unknown parameters.


Display output to


Regression Line:
Correlation:
R-squared:
for $\mu_y$ at $x=$:
for $y$ at $x=$:


Residual Plot
Residuals $y-\hat{y}$
Regression Inference: $y=\alpha+\beta x$
Degrees of Freedom: $df=n-2=$
Estimate of Slope:
Standard Error Slope:
Regression Standard Error:
$t$-Statistic:
% Confidence Interval for $\beta$:
$p$-value:$p=$