What is the Q-Q plot in linear regression model?
As it is clear with name, the Q-Q plot is a graphical plotting of the quantiles of two distributions with respect to each other. In other words we can say plot quantiles against quantiles. Whenever we are interpreting a Q-Q plot, we shall concentrate on the ‘y = x’ line. We also call it the 45-degree line in statistics. It entails that each of our distributions has the same quantiles. In case if we witness a deviation from this line, one of the distributions could be skewed when compared to the other.
Here is an example, where we are generating data x from a Gamma distribution with shape = 2 and rate = 1 parameter.
# Set seed for reproducibility
set.seed(2017);
# Generate some Gamma distributed data
x <- rgamma(100, shape = 2, rate = 1);
# Sort x values
x <- sort(x);
# Theoretical distribution
x0 <- qgamma(ppoints(length(x)), shape = 2, rate = 1);
plot(x = x0, y = x, xlab = "Theoretical quantiles", ylab = "Observed quantiles");
abline(a = 0, b = 1, col = "red");
Above code will output like this: