Why do we need normality assumption for residuals?

The important point in the normality assumption is that it enables us to derive the sampling distribution of β0 and β1 and σ2. This test for the normality is an asymptotic or large-sample test. It is based on the OLS residuals just like the chi-square test.

What does the assumption normality of residuals mean?

The normality assumption, now, says that the difference between the Ys and their matching E[Y|X] follows a normal distribution with mean zero.

Why is data normality important?

They provide simple summaries about the sample and the measures. Measures of the central tendency and dispersion are used to describe the quantitative data. For the continuous data, test of the normality is an important step for deciding the measures of central tendency and statistical methods for data analysis.

Why does linear regression assume normality?

The normality assumption relates to the distributions of the residuals. This is assumed to be normally distributed, and the regression line is fitted to the data such that the mean of the residuals is zero. To examine whether the residuals are normally distributed, we can compare them to what would be expected.

How important is normality?

For the continuous data, test of the normality is an important step for deciding the measures of central tendency and statistical methods for data analysis. When our data follow normal distribution, parametric tests otherwise nonparametric methods are used to compare the groups.

Why is it important to have normally distributed errors?

One reason this is done is because the normal distribution often describes the actual distribution of the random errors in real-world processes reasonably well. Of course, if it turns out that the random errors in the process are not normally distributed, then any inferences made about the process may be incorrect.

Why are assumptions important in testing?

Many statistical tests have assumptions that must be met in order to insure that the data collected is appropriate for the types of analyses you want to conduct. Failure to meet these assumptions, among others, can result in inaccurate results, which is problematic for many reasons.

What is the purpose of normality test?

In statistics, normality tests are used to determine if a data set is well-modeled by a normal distribution and to compute how likely it is for a random variable underlying the data set to be normally distributed.