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Multiple Linear Regression Calculator



  • Values of the response variable $y$ vary according to a normal distribution with standard deviation $\sigma$ for any values of the explanatory variables $x_1, x_2,\ldots,x_k.$ 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 variables $x_1, x_2,\ldots,x_k$ is linear and is given by $\mu_y=\beta_0+\beta_1 x_1+\cdots +\beta_k x_k$ where each $\beta_i$ is an unknown parameter.
Resp. Var. $y$ Expl. Var. $x_1$ Expl. Var. $x_2$
Variable Names (optional):
Sample data goes here (enter numbers in columns):


Model:$y=\beta_0 + \beta_1 x_1 +\beta_2 x_2$



Display output to

IncludeInteraction
$x_1$*$x_1$
$x_1$*$x_2$
$x_2$*$x_2$






Summary of Overall Fit



Analysis of Variance Table

SourcedfSSMS$F$-statistic$p$-value
Regression
Residual Error
Total




Histogram of the Residuals
Percent
Residuals




Normal Probability Plot of Residuals
Residual Quantiles
Standard Normal Quantiles




Five Number Summary of Residuals

Minimum:
1st Quartile:
Median:
3rd Quartile:
Maximum: