Statistics - Assumptions underlying correlation and regression analysis (Never trust summary statistics alone)

1 - About

The magnitude of a correlation depends upon many factors, including:

3 - Anscombe's quartet

In 1973, statistician Dr. Frank Anscombe developed a classic example to illustrate several of the assumptions underlying correlation and linear regression.

The below scatter-plots have the same correlation coefficient and thus the same regression line.

They have also the same mean and variance.

<MATH> Y = 3 + 0.5 X </MATH>

Only the first one on the upper left satisfies the assumptions underlying a:

4 - Datasaurus: Never trust summary statistics alone; always visualize your data

The Datasaurus Dozen. While different in appearance, each dataset has the same summary statistics (mean, standard deviation, and Pearson's correlation) to two decimal places.


5 - How to

5.1 - test the assumptions in a regression analysis ?

To test the assumptions in a regression analysis, we look a those residual as a function of the X productive variable. (X remaining on the X axis and the residuals coming on the Y axis).

For each of the individual, the residual can be calculated as the difference between the predicted score and a actual score.

If the assumptions are good, there must be:

  • no relationship between X and the residual. They must be independent. The relation coefficient must be zero.
  • some of the points above zero and some of them below zero. It will indicate Homoscedasticity
data_mining/regression_correlation_assumption.txt · Last modified: 2017/09/13 16:04 by gerardnico