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

You may copy data from Excel, Google sheets or any tool that separate data with Tab and Line Feed. Copy the data, one block of consecutive columns includes the header, and paste below. Y must be the right column (more) . click to see example:

Reporting results in APA style

Correlation matrix (pearson)

ANOVA table

anova

tresults2

validation message

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 = b_{0} + b_{1}X_{1} + b_{2}X_{2} + b_{3}X_{3}+...+ b_{p}X_{p} + ε It is easier to use the matrix form for multiple linear regression calculations: Y = XB + Ε Ŷ = XB B = (X'X)^{-1}X'Y

[1 X_{11} X_{12} ... X_{1p}]

[Y_{1]}

ε_{1}]

[1 X_{21} X_{22} ... X_{2p}]

[Y_{2]}

[ε_{2}]

X =

[1 X_{31} X_{32} ... X_{3p}]

Y =

[Y_{3}]

Ε =

[ε_{3}]

[1 X_{41} X_{42} ... X_{4p}]

[Y_{4]}

[ε_{4}]

[1 X_{n1} X_{n2} ... X_{np}]

[Y_{n}]

[ε_{n}]

[B_{0}]

[B_{1}]

B =

[B_{2}]

[... ]

[B_{p}]

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

Hypotheses

H_{0}: Y = b_{0}

H_{1}: Y=b_{0}+b_{1}X_{1}+...+b_{p}X_{p}

Test statistic

F distribution

R Code

The following R code should produce the same results: