Comparing a linear regression with a log-linear regression with R

Question

I have a model in R where I have regressed the price of a Honda civic on its mileage:

civic <- read.csv("civic.csv")
c <- civic

plot (c$Mileage, c$Price,
      xlab = "Mileage",
      ylab = "Price")

regrPM1 <- lm(Price~Mileage, data = c)

abline (regrPM1, col="red",lwd=3)

This gives me the following:

So far so good. Now I have another model:

regrPM2 <- lm(log(c$Price)~c$Mileage)

And I want to add the corrosponding regression line into the Plot1 from above. When I use the abline command:

abline(regrPM2, col="green", lwd=3)

It results in the following plot:

Now this can't be used to compare the two models. I am looking for a way to compare them without using a 'log' scale. I think, I could use the curve demand to get better results but that did not worked out yet.

Thankful for any kind of help!

Answer 1

It's not a straight line on the original scale. You could do something along the lines of the following to show the non-linear prediction on the original scale.

DF <- data.frame(Mileage=seq(1, 150000, 1))
pred <- predict(regrPM2, newdata=DF)
lines(DF$Mileage, exp(pred))

This must be run after you create the initial plot with plot()

Answer 2

It's difficult to demonstrate what's wrong here without data, so I'll try to create some that's roughly similar to yours:

set.seed(69)

m <- rgamma(5000, 2, 2) * 30000
p <- 3e4 * log((rnorm(5e3, 1e4, 1e3) + m)/(m + rnorm(5e3, 5e3, 5e2)) + rgamma(5000, 2, 2)/8)

c <- data.frame(Mileage = m, Price = p)

plot (c$Mileage, c$Price,
      xlab = "Mileage",
      ylab = "Price")

This is close enough for demonstration purposes.

Now we can add the linear regression line using your code:

regrPM1 <- lm(Price~Mileage, data = c)

abline (regrPM1, col="red",lwd=3)

Now, if we regress the log of the price on the mileage, we will get the same flat green line as you did if we just plot the result using abline :

regrPM2 <- lm(log(c$Price)~c$Mileage)
abline(regrPM2, col="green", lwd=3)

That's because we are plotting the log of the price on the (non-logged) plot. We want to take the anti-log of the result of our regression and plot that.

Note that it's better to use the data argument in our lm call, so let's do:

regrPM3 <- lm(log(Price) ~ Mileage, data = c)

Now instead of trying to plot this as a straight line, let's take the anti-log of its predictions at fixed intervals and plot them:

lines(seq(0, 2e5, 1e3), 
      exp(predict(regrPM3, newdata = list(Mileage = seq(0, 2e5, 1e3)))),
      col = "blue", lty = 2, lwd = 4)

So the blue dotted line is what the log regression looks like.