The magnitude of a correlation depends upon many factors, including:
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:
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.
See:
Most of the examples of using linear regression just show a regression line with some dataset. it's much more fun to understand it by drawing data in. Bring your own doodles linear regression
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: