chart.QQPlot: Plot a QQ chart in PerformanceAnalytics: Econometric Tools for Performance and Risk Analysis (2024)

FAQs

What is the plot of a Q-Q plot? ›

A QQ plot is a scatterplot created by plotting two sets of quantiles against one another. If both sets of quantiles came from the same distribution, we should see the points forming a line that's roughly straight.

A Q-Q plot can be used in regression models to check some of the assumptions that are required for valid inference. For example, you can use a Q-Q plot to check if the residuals of the model are normally distributed, which is an assumption for many parametric tests and confidence intervals.

Examining data distributions using QQ plots

Points on the Normal QQ plot provide an indication of univariate normality of the dataset. If the data is normally distributed, the points will fall on the 45-degree reference line. If the data is not normally distributed, the points will deviate from the reference line.

A Q-Q (Quantile-Quantile) plot is another graphic method for testing whether a dataset follows a given distribution. It differs from the probability plot in that it shows observed and expected values instead of percentages on the X and Y axes.

If the two distributions being compared are identical, the Q–Q plot follows the 45° line y = x. If the two distributions agree after linearly transforming the values in one of the distributions, then the Q–Q plot follows some line, but not necessarily the line y = x.

Q-Q plots are also used to find the skewness (a measure of asymmetry) of a distribution. When we plot theoretical quantiles on the x-axis and the sample quantiles whose distribution we want to know on the y-axis, then we see a very peculiar shape of a normally distributed Q-Q plot for skewness.

Let's start with the plot that is already familiar to us: the Normal Q-Q plot. We can use this plot to check for Assumption 3 (Normality). Aside from one outlier (observation 11), the dots follow the line very closely.

Answer and Explanation:

If the ordered values fall on a straight line on the q-q plot, then it is assumed that the data come from normally distributed populations. The plot is used to formally test the null hypothesis that data are normally distributed.

Q-Q Plot for Evaluating Multivariate Normality and Outliers

The basic idea is the same as for a normal probability plot. For multivariate data, we plot the ordered Mahalanobis distances versus estimated quantiles (percentiles) for a sample of size n from a chi-squared distribution with p degrees of freedom.

Technically speaking, a Q-Q plot compares the distribution of two sets of data. In most cases, a probability plot will be most useful. A probability plot compares the distribution of a data set with a theoretical distribution. The R function qqnorm( ) compares a data set with the theoretical normal distibution.

What are the disadvantages of Q-Q plot? ›

Quantile-Quantile (Q-Q) plots are often difficult to interpret because it is unclear how large the deviation from the theoretical distribution must be to indicate a lack of fit.

QQ-Plots are a more robust test for normality and provide visual feedback on the nature of the data. It is also recommended to histogram the data to see if it appears normal. If the points in the Q-Q plot are on a line from the lower left to the upper right then the data is basically normally distributed.

The Q-Q boxplot is an amalgam of the boxplot and the Q-Q plot and allows the user to rapidly examine summary statistics and tail behavior for multiple distributions in the same pane. As an extension of the 'ggplot2' implementation of the boxplot, possible modifications to the boxplot extend to the Q-Q boxplot.

The slope of the Q-Q plot reflects the ratio of the standard deviation of your data to the standard deviation of the normal distribution. If the slope is greater than 1, it means that your data are more spread out than the normal distribution, and vice versa.