Ordinary least squares regression.
Arguments
- object
An object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted or class
lm.- ...
Other inputs.
Value
ols_regress returns an object of class "ols_regress".
An object of class "ols_regress" is a list containing the following
components:
- r
square root of rsquare, correlation between observed and predicted values of dependent variable
- rsq
coefficient of determination or r-square
- adjr
adjusted rsquare
- rmse
root mean squared error
- cv
coefficient of variation
- mse
mean squared error
- mae
mean absolute error
- aic
akaike information criteria
- sbc
bayesian information criteria
- sbic
sawa bayesian information criteria
- prsq
predicted rsquare
- error_df
residual degrees of freedom
- model_df
regression degrees of freedom
- total_df
total degrees of freedom
- ess
error sum of squares
- rss
regression sum of squares
- tss
total sum of squares
- rms
regression mean square
- ems
error mean square
- f
f statistis
- p
p-value for
f- n
number of predictors including intercept
- betas
betas; estimated coefficients
- sbetas
standardized betas
- std_errors
standard errors
- tvalues
t values
- pvalues
p-value of
tvalues- df
degrees of freedom of
betas- conf_lm
confidence intervals for coefficients
- title
title for the model
- dependent
character vector; name of the dependent variable
- predictors
character vector; name of the predictor variables
- mvars
character vector; name of the predictor variables including intercept
- model
input model for
ols_regress
Interaction Terms
If the model includes interaction terms, the standardized betas are computed after scaling and centering the predictors.
References
https://www.ssc.wisc.edu/~hemken/Stataworkshops/stdBeta/Getting%20Standardized%20Coefficients%20Right.pdf
Examples
ols_regress(mpg ~ disp + hp + wt, data = mtcars)
#> Model Summary
#> ---------------------------------------------------------------
#> R 0.909 RMSE 2.468
#> R-Squared 0.827 MSE 6.964
#> Adj. R-Squared 0.808 Coef. Var 13.135
#> Pred R-Squared 0.768 AIC 158.643
#> MAE 1.907 SBC 165.972
#> ---------------------------------------------------------------
#> RMSE: Root Mean Square Error
#> MSE: Mean Square Error
#> MAE: Mean Absolute Error
#> AIC: Akaike Information Criteria
#> SBC: Schwarz Bayesian Criteria
#>
#> ANOVA
#> --------------------------------------------------------------------
#> Sum of
#> Squares DF Mean Square F Sig.
#> --------------------------------------------------------------------
#> Regression 931.057 3 310.352 44.566 0.0000
#> Residual 194.991 28 6.964
#> Total 1126.047 31
#> --------------------------------------------------------------------
#>
#> Parameter Estimates
#> ----------------------------------------------------------------------------------------
#> model Beta Std. Error Std. Beta t Sig lower upper
#> ----------------------------------------------------------------------------------------
#> (Intercept) 37.106 2.111 17.579 0.000 32.782 41.429
#> disp -0.001 0.010 -0.019 -0.091 0.929 -0.022 0.020
#> hp -0.031 0.011 -0.354 -2.724 0.011 -0.055 -0.008
#> wt -3.801 1.066 -0.617 -3.565 0.001 -5.985 -1.617
#> ----------------------------------------------------------------------------------------
# if model includes interaction terms set iterm to TRUE
ols_regress(mpg ~ disp * wt, data = mtcars, iterm = TRUE)
#> Model Summary
#> ---------------------------------------------------------------
#> R 0.922 RMSE 2.296
#> R-Squared 0.850 MSE 6.027
#> Adj. R-Squared 0.834 Coef. Var 12.219
#> Pred R-Squared 0.801 AIC 154.018
#> MAE 1.897 SBC 161.346
#> ---------------------------------------------------------------
#> RMSE: Root Mean Square Error
#> MSE: Mean Square Error
#> MAE: Mean Absolute Error
#> AIC: Akaike Information Criteria
#> SBC: Schwarz Bayesian Criteria
#>
#> ANOVA
#> --------------------------------------------------------------------
#> Sum of
#> Squares DF Mean Square F Sig.
#> --------------------------------------------------------------------
#> Regression 957.299 3 319.100 52.947 0.0000
#> Residual 168.749 28 6.027
#> Total 1126.047 31
#> --------------------------------------------------------------------
#>
#> Parameter Estimates
#> ----------------------------------------------------------------------------------------
#> model Beta Std. Error Std. Beta t Sig lower upper
#> ----------------------------------------------------------------------------------------
#> (Intercept) 44.082 3.123 14.115 0.000 37.685 50.479
#> disp -0.056 0.013 -0.385 -4.257 0.000 -0.083 -0.029
#> wt -6.496 1.313 -0.616 -4.946 0.000 -9.186 -3.805
#> disp:wt 0.012 0.003 0.278 3.596 0.001 0.005 0.018
#> ----------------------------------------------------------------------------------------