A normal probability plot is a visual check of normality. The EditGrid example below uses data from the lotto example in Gujarati's Econometrics text. The OLS line regresses weekly lotto spend (Y) against disposable income (X); the Fitted Y is the regression line. The residual (e) is the difference between the actual Y and the regression line (observed Y - Fitted Y = e).

The normal probability plot is then a visual test of whether the residuals are normally distributed. Recall a criteria of the classic linear regression model is that the error term follows a normal distribution with mean (expected value) of zero and constant variance.

The actual normal probability plot is the chart below. The straight line is the benchmark: the residual would match this line if it were normal. The actual pattern of the residual is the curvy line. As such, it visually shows fat tails. The calculations are below the chart. The first step is to sort the residuals. These sorted residuals become the X-axis. Then two Y-series are plotted: an inverse standard normal (the benchmark) and the the actual standardized values.

EditGrid:

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