Linear Regression in R using Principal Component Regression

Linear regression is a statistical method that helps to understand the relationship between a dependent variable and one or more independent variables. It is represented by an equation in the form of Y = a + bX, where Y is the dependent variable, X is the independent variable, a is the y-intercept and b is the slope of the line. It helps to make predictions about the dependent variable, based on the values of the independent variables.

Principal Component Regression (PCR) is a variation of linear regression that uses a technique called principal component analysis (PCA) to reduce the number of independent variables. PCA is a method for transforming a set of correlated variables into a smaller set of uncorrelated variables, called principal components.

The idea behind PCR is to use the principal components as independent variables instead of the original independent variables. The principal components are chosen such that they explain the maximum variance in the data. This can help to reduce the number of independent variables, which can improve the performance of linear regression, especially when the original data is high-dimensional and has multicollinearity.

In PCR, we first perform PCA on the independent variables. This will generate a set of principal components, which are then used as independent variables in linear regression.

It’s important to note that PCR is not always better than the regular linear regression, it depends on the data and the problem at hand. Also, PCR assumes that the principal components are linear combinations of the original independent variables.

Another important aspect, PCR is just a linear regression, so it assumes that the relationship between the independent and dependent variables is linear. If the relationship is non-linear, PCR may not provide accurate results.

In this Data Science Recipe, you will learn: Linear Regression in R using Principal Component Regression.