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What is QQ Plot?

A QQ Plot, which stands for "Quantile-Quantile Plot," is a graphical tool used in statistics to assess whether a dataset follows a particular theoretical distribution, such as a normal distribution. It is particularly helpful for checking the normality assumption of a dataset. Here's how a QQ Plot works:

1. Theoretical Quantiles: On the x-axis of the plot, theoretical quantiles are plotted. These are the expected quantiles of the chosen theoretical distribution, often the normal distribution. The quantiles are calculated based on the theoretical distribution's parameters (mean and standard deviation).

2. Sample Quantiles: On the y-axis of the plot, the sample quantiles of the dataset being analyzed are plotted. These quantiles represent the observed values in the dataset, sorted in ascending order.

In an ideal situation where the dataset perfectly follows the theoretical distribution (e.g., a perfect normal distribution), the points on the QQ Plot should form a straight line with a slope of 45 degrees. Deviations from this line can indicate departures from the assumed distribution.

Interpreting a QQ Plot:

- If the points closely follow a straight 45-degree line, it suggests that the dataset's distribution is similar to the assumed distribution (e.g., normal).

- If the points deviate from the straight line, it indicates a departure from the assumed distribution. For example, if the points bend upward, it suggests heavier tails than the assumed distribution. If they bend downward, it suggests lighter tails.

QQ Plots are a valuable tool for assessing the normality of data, detecting skewness, and identifying outliers. They are commonly used in various statistical analyses, such as regression analysis, hypothesis testing, and quality control, to verify whether the data meets the underlying assumptions of the chosen statistical model.

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