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What is Q-Q plot in linear regression?
Quantile-Quantile (Q-Q) plot, is a graphical tool to help us assess if a set of data plausibly came from some theoretical distribution such as a Normal, exponential or Uniform distribution. Also, it helps to determine if two data sets come from populations with a common distribution.
Should I use PP plot or Q-Q plot?
A P-P plot compares the empirical cumulative distribution function of a data set with a specified theoretical cumulative distribution function F(·). A Q-Q plot compares the quantiles of a data distribution with the quantiles of a standardized theoretical distribution from a specified family of distributions.
How is a Q-Q plot used in statistics?
In Statistics, Q-Q (quantile-quantile) plots play a very vital role to graphically analyze and compare two probability distributions by plotting their quantiles against each other. If the two distributions which we are comparing are exactly equal then the points on the Q-Q plot will perfectly lie on a straight line y = x.
How is the slope of a QQ plot determined?
The linearity of the QQ-plot only suggests that your sample follows a normal distribution (or more specifically, it’s quantile function is the probit function). The slope is determined by the standard deviation (for sd=1, we get the popular x = y line).
A point (x, y) on the plot corresponds to one of the quantiles of the second distribution ( y -coordinate) plotted against the same quantile of the first distribution ( x -coordinate). Thus the line is a parametric curve with the parameter which is the number of the interval for the quantile.
What does a skewed Q-Q plot look like?
First we plot a distribution that’s skewed right, a Chi-square distribution with 3 degrees of freedom, against a Normal distribution. Notice the points form a curve instead of a straight line. Normal Q-Q plots that look like this usually mean your sample data are skewed. Next we plot a distribution with “heavy tails” versus a Normal distribution: