Topic 7 Linear Regression

Introduction

• Regression analysis is one of the most widely used tool in quantitative research which is used to analyse the relationship between variables.

• One or more variables are considered to be explanatory variables, and the other is considered to be the dependent variable.

• In general linear regression is used to predict a continuous dependent variable (regressand) from a number of independent variables (regressors) assuming that the relationship between the dependent and independent variables is linear.

• If we have a dependent (or response) variable Y which is related to a predictor variables \(X_{i}\). The simple regression model is given by

\[\begin{equation} Y=\alpha+\beta X_{i}+\epsilon_{i} \tag{7.1} \end{equation}\]

• R has the function \(\mathtt{lm}\) (linear model) for linear regression.

• The main arguments to the function \(\mathtt{lm}\) are a formula and the data. \(\mathtt{lm}\) takes the defining model input as a formula

• A formula object is also used in other statistical function like \(\mathtt{glm,\,nls,\,rq}\) etc, which is from a formula class.