Linear Regression: Introduction
Which one of the following best represents the goal(s) of linear regression?
-Given data points {(Xi, Yi)} , try to explain why Y is changing depending on X.
-Given data points {(Xi, Yi)} , fit a model and try to predict Y given a value for X .
-Given data points {(Xi, Yi)}, prove that the relationship between Y and X is linear.
-Given data points {(Xi, Yi)}, obtain the functional relationship between Y and X.
The correct answer is:
-Given data points {(Xi, Yi)} , fit a model and try to predict Y given a value for X.
Linear regression is a statistical modeling technique used to understand the relationship between a dependent variable (Y) and one or more independent variables (X). The goal of linear regression is to find the best-fitting line (or curve) that describes the relationship between the variables. The model is then used to predict the value of the dependent variable given specific values of the independent variable(s).
To achieve this goal, linear regression estimates the parameters of the linear equation that represents the relationship between the variables. It uses the data points ({(Xi, Yi)}) to find the line that minimizes the difference between the observed values of Y and the predicted values from the model. Once the model is fitted, it can be used to make predictions for new values of X.