Multiple linear Regression Calculator

*Include
Transform
Groups	X1	X2	Y
Data
P-value:
Average:
n:
S:
Skewness:
Normality:**
Outliers:

Header: You may change the groups' names to their real names.
Data: When entering data, press Enter or Comma , or Space after each value.
* All variables will be included in the automatic iterations mode.
** Normality colors based on α=0.05

Reporting results in APA style

Multiple linear regression calculator

The calculator uses variables transformations, calculates the Linear equation, R, p-value, outliers and the adjusted Fisher-Pearson coefficient of skewness.
After checking the residuals' normality, multicollinearity, homoscedasticity and priori power, the program interprets the results.
Then, it draws a histogram, a residuals QQ-plot, a correlation matrix, a residuals x-plot and a distribution chart.
You may transform the variables, exclude any predictor or run backward stepwise selection automatically based on the predictor's p-value.

Right-tailed F test. Checks if the entire regression model is statistically significant. Why?

Multiple linear regression formula

Y = b₀ + b₁X₁ + b₂X₂ + b₃X₃+...+ b_pX_p + ε
It is easier to use the matrix form for multiple linear regression calculations:
Y = XB + Ε
Ŷ = XB
B = (X'X)^-1X'Y

	[1 X₁₁ X₁₂ ... X_1p]		[Y_1]		ε₁]
	[1 X₂₁ X₂₂ ... X_2p]		[Y_2]		[ε₂]
X =	[1 X₃₁ X₃₂ ... X_3p]	Y =	[Y₃]	Ε =	[ε₃]
	[1 X₄₁ X₄₂ ... X_4p]		[Y_4]		[ε₄]
	[1 X_n1 X_n2 ... X_np]		[Y_n]		[ε_n]

	[B₀]
	[B₁]
B =	[B₂]
	[... ]
	[B_p]

Y - dependent variable vector.
Ŷ - predicted Y vector.
Ε - residuals vector, Ε = Y - Ŷ.
p - number of predictors.
n - sample size.

Hypotheses

H₀: Y = b₀

H₁: Y=b₀+b₁X₁+...+b_pX_p

Test statistic

F distribution

Multiple Linear Regression Calculator

Reporting results in APA style

Multiple linear regression calculator

Multiple linear regression formula

R Code



Groups	Pred Y	Residual
Data
pval:
avg:
n:
S:
Skewness
Normality
Outliers