The sample p-th percentile of any data set is, roughly speaking, the value such that p% of the measurements fall below the value. Here's a screencast illustrating how the p-th percentile value reduces to just a normal score. The p-th percentile value reduces to just a " Z-score" (or "normal score"). Once you do that, determining the percentiles of the standard normal curve is straightforward. Statistical theory says its okay just to assume that \(\mu = 0\) and \(\sigma^2 = 1\). And, of course, the parameters \(\mu\) and σ 2 are typically unknown. The problem is that to determine the percentile value of a normal distribution, you need to know the mean \(\mu\) and the variance \(\sigma^2\). Here's a screencast illustrating a theoretical p-th percentile. The theoretical p-th percentile of any normal distribution is the value such that p% of the measurements fall below the value. If a normal probability plot of the residuals is approximately linear, we proceed assuming that the error terms are normally distributed. Here's the basic idea behind any normal probability plot: if the error terms follow a normal distribution with mean \(\mu\) and variance \(\sigma^2\), then a plot of the theoretical percentiles of the normal distribution versus the observed sample percentiles of the residuals should be approximately linear. In this section, we learn how to use a " normal probability plot of the residuals" as a way of learning whether it is reasonable to assume that the error terms are normally distributed. Recall that the third condition - the "N" condition - of the linear regression model is that the error terms are normally distributed.
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