Regression Analysis — Normality

Histogram and Stem & Leaf plot - Regression analysis

Exhibit 33.27 Histogram and Stem & Leaf plot reveals the shape of the distribution. The Stem & Leaf plots also enumerates the actual values. (Source: SPSS).

Normal probability plot and the de-trended normal probability plot - Regression analysis

Exhibit 33.28 The normal probability plot and the de-trended normal probability plot. (Source: SPSS).

The dependent and independent variables are assumed to follow normal distribution. Furthermore, in the case of multiple regression, this assumption is also applicable to the combination of variables.

If their distributions vary substantially from the normal distribution, the F test, which assesses the overall regression, and the t-test, which assesses statistical significance of the coefficients, may no longer remain valid. These tests assume that the residuals are distributed normally.

Univariate normality can be visually examined through the histogram and the stem & leaf plot (Exhibit 33.27), though this may be problematic for smaller samples. The normal probability plot, Exhibit 33.28, is a more reliable check. This compares the cumulative distribution of the data with that for a normal distribution. If data is normal, it is scattered close to the diagonal which represents the theoretical normal distribution.

Additionally, the Kurtosis statistic tests for “peakedness” or “flatness” of the data, and the skewness statistic is a measure for skewness.

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