cars2=cars;
cars2$dist=qnorm(pmin(0.999,pmax(0.001,rank(cars2$dist)/length(rank(cars2$dist)))))

map=(quantile(cars$dist,probs = seq(0.001,0.999,0.001)))

require(datasets)

hist(cars$speed)
    hist(cars$dist)
m=lm(dist~speed,cars)
fit=predict(m)
skewness(cars$dist)
summary(m)

cars2=cars;
cars2$dist=qnorm(pmin(0.999,pmax(0.001,rank(cars2$dist)/length(rank(cars2$dist)))))
    map=(quantile(cars$dist,probs = seq(0.001,0.999,0.001)))
hist(cars2$dist)
    skewness(cars2$dist)
length(map)
hist(map)
m3=lm(dist~speed,cars2);
m3=stepAIC(m3,trace=F)
summary(m3)
data=round(pnorm(predict(m3))*1000)
range(data)
fit2=map[data]
plot(cars$dist,fit2,col="blue")
    points(cars$dist,fit,col="red")

rmse=function(x,y,k=0){
  return( sqrt(sum((x-y)^2)/(length(x)-k)));
}
rmse(cars$dist,fit)
    rmse(cars$dist,fit2)