16 Multiple regression & model fitting
16.1 MLR
This is very similar to simple regression, but you can add in extra predictors:
For example, this will predict sepal length, using TWO predictors (width and petal length). See the MLR lecture for interpretation.
MLRmodel <- lm(Sepal.Length ~ Sepal.Width + Petal.Length ,data=iris)
ols_regress(MLRmodel)## Model Summary
## ---------------------------------------------------------------
## R 0.917 RMSE 0.330
## R-Squared 0.840 MSE 0.111
## Adj. R-Squared 0.838 Coef. Var 5.704
## Pred R-Squared 0.834 AIC 101.025
## MAE 0.266 SBC 113.068
## ---------------------------------------------------------------
## 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 85.840 2 42.920 386.386 0.0000
## Residual 16.329 147 0.111
## Total 102.168 149
## ---------------------------------------------------------------------
##
## Parameter Estimates
## --------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## --------------------------------------------------------------------------------------
## (Intercept) 2.249 0.248 9.070 0.000 1.759 2.739
## Sepal.Width 0.596 0.069 0.313 8.590 0.000 0.459 0.733
## Petal.Length 0.472 0.017 1.006 27.569 0.000 0.438 0.506
## --------------------------------------------------------------------------------------