EAS Publications Series
Volume 66, 2014Statistics for Astrophysics Methods and Applications of the Regression
|Page(s)||19 - 39|
|Published online||23 January 2015|
D. Fraix-Burnet and D. Valls-Gabaud (eds)
EAS Publications Series, 66 (2014) 19–39
Simple Linear Regression
Laboratory LJK, Grenoble University, BP. 53, 38041 Grenoble Cedex 09, France
This chapter deals with the very simple situation where the mean of a variable, the response variable, usually denoted Y, is linearly depending on another variable, the regressor, here denoted x1. The least squared method is used to get the parameter estimators and estimates of their precisions. This leads to design confidence and prediction intervals, significance tests, anova table. Residuals, diagnostics to identify influent observations and outliers are presented. Methods to detect departures from the model's assumptions and ways of dealing with these departures are addressed.
Along the chapter a data set is used to illustrate the methods with the sofware R.
© EAS, EDP Sciences, 2015