Linear Regression and Correlation

Abstract

The objective of many statistical analysis is to make predictions. For example, in canola cultivation it may be of interest to predict the canola crop yield (the dependent or response variable) for different levels of nitrogen fertilizer (the independent or explanatory variable). Such prediction require to find a mathematical formula (a statistical model) which relates the dependent variable to one or more independent variables. In countless real-world problems such relationship is not deterministic: it must be a random component to the formula that relates the variables. The set of statistical methods for finding the best relationship between response and explanatory variables is known as regression analysis. In this chapter we first describe method of least squares to find the linear relationship, i.e. simple and multiple linear regression model which is illustrated with suggestive examples. Then, the correlation analysis used to quantify the association between variables is presented.