Regression analysis
Regression analysis is a field of statistics. It is a tool to show the relationship between the inputs and the outputs of a system. Regression analysis is often used for prediction of trends. It is also used for studying whether one thing causes another.
The first type of regression analysis was linear regression. The method of least squares was first published by Legendre in 1805[1] and in 1809 by Gauss.[2] Both used the method to predict the movement of planets around the sun. Gauss published an improved method in 1821.
Regression Analysis Media
Regression line for 50 random points in a Gaussian distribution around the line y=1.5x+2
Illustration of linear regression on a data set
In the middle, the fitted straight line represents the best balance between the points above and below this line. The dotted straight lines represent the two extreme lines, considering only the variation in the slope. The inner curves represent the estimated range of values considering the variation in both slope and intercept. The outer curves represent a prediction for a new measurement.
Related pages
References
- ↑ A.M. Legendre. Nouvelles méthodes pour la détermination des orbites des comètes (1805). “Sur la Méthode des moindres quarrés” is an appendix.
- ↑ C.F. Gauß. Theoria Motus Corporum Coelestium in Sectionibus Conicis Solem Ambientum. (1809)