Loading the packages

library(webrSub)
library(predict3d)

Simple linear regression

fit=lm(mpg~wt,data=mtcars)
ggPredict(fit)

cat(result=explain(fit))
The predictor variable 'wt' accounts for 75.28 % of the total variation of your dependent variable 'mpg'. Your R^2 is quite good. The coefficient for 'wt' is smaller than zero. This means that the value of your dependent variable 'mpg' decreases by 5.34 for any increase of 1 in your independent variable 'wt'. The coefficient is  significantly different from zero(p< 0.001). The predicted value of dependent variable 'mpg' is calculated by the equation: '37.29 - 5.34*wt'.

Polynomial regression

fit=lm(mpg~wt+I(wt^2),data=mtcars)
ggPredict(fit)

cat(explain(fit))
The predictor variables 'wt','I(wt^2)' account for 81.91 % of the total variation of your dependent variable 'mpg'. Your R^2 is quite good. The coefficient for 'wt' is  significantly different from zero(p< 0.001) The coefficient for 'I(wt^2)' is  significantly different from zero(p =0.003) The predicted value of dependent variable 'mpg' is calculated by the equation: '49.93 - 13.38*wt + 1.17*I(wt^2)'.

Multiple linear regression

fit=lm(mpg~hp+wt+am,data=mtcars)
ggPredict(fit)

cat(explain(fit))
The predictor variables 'hp','wt','am' account for 83.99 % of the total variation of your dependent variable 'mpg'. Your R^2 is quite good. The coefficient for 'hp' is smaller than zero. This means that the value of your dependent variable 'mpg' decreases by 0.037 for any increase of 1 in your independent variable 'hp', if 'wt','am' remain(s) constant. The coefficient is  significantly different from zero(p< 0.001), controlling for the other variable(s). The coefficient for 'wt' is smaller than zero. This means that the value of your dependent variable 'mpg' decreases by 2.88 for any increase of 1 in your independent variable 'wt', if 'hp','am' remain(s) constant. The coefficient is  significantly different from zero(p =0.004), controlling for the other variable(s). The coefficient for 'am' is larger than zero. This means that the value of your dependent variable 'mpg' increases by 2.08 for any increase of 1 in your independent variable 'am', if 'hp','wt' remain(s) constant. The coefficient is  not significantly different from zero(p =0.141) suggesting that 'am' and 'mpg' are not linearly related when controlling for other predictor variable(s). The predicted value of dependent variable 'mpg' is calculated by the equation: '34.00 - 0.04*hp - 2.88*wt + 2.08*am'.

Multiple linear regression with interaction

fit=lm(mpg~hp*wt,data=mtcars)
ggPredict(fit)

cat(explain(fit))
The predictor variables 'hp','wt' and the interaction 'hp:wt' account for 88.48 % of the total variation of your dependent variable 'mpg'. Your R^2 is quite good. The interaction between 'hp' and 'wt' is significant. This means that the relationship between one predictor and the response variable depends on the level of the other variable(s). Here it means that the relationship between 'mpg' and 'hp' varies by 'wt'. The predicted value of dependent variable 'mpg' is calculated by the equation: '49.81 - 0.12*hp - 8.22*wt + 0.03*hp*wt' which simplifies to '49.81 - 8.22*wt + (-0.12 + 0.03*wt)*hp'. If 'wt' is 2.24, the value of your dependent variable 'mpg' decreases by 0.058 for any increase of 1 in your independent variable 'hp' If 'wt' is 3.22, the value of your dependent variable 'mpg' decreases by 0.031 for any increase of 1 in your independent variable 'hp' If 'wt' is 4.2, the value of your dependent variable 'mpg' decreases by 0.0033 for any increase of 1 in your independent variable 'hp'