# Understanding  Linear Regression

Linear Regression is a statistical method used to establish a linear relationship between two variables, namely the dependent variable (y) and the independent variable (x). This method takes into account the relationship between both variables by calculating the slope coefficient, which confirms how a change in the independent variable impacts changes in the dependent variable.

In this SEO post, we will explore some essential aspects and frequently asked questions about Linear Regression while explaining in simple terms.

## What is Linear Regression?

Linear Regression is a statistical technique that maps out relationships between variables. It helps predict outcomes of variables based on other variables. It helps us understand the impact of one variable on another, where one is dependent on another.

## What are Dependent and Independent Variables?

A Dependent Variable is a variable that cannot function without some help from other variables. In contrast, an Independent Variable can stand alone as its own entity; its value does not depend on any other variable.

In linear regression, the dependent variable represents what we want to predict or understand better, based on given independent variables. For instance, if we want to determine the influence of education on earning, education would be our independent variable while earning would be our dependent variable.

## What is the Regression Equation?

The Regression Equation used in linear regression analysis is used to generate predictions for dependent variables based on independent variables. The regression equation establishes an equation that predicts how much change there will be in one of your Y's for every change in x.

## What are Residuals?

Residuals are simply the differences between actual values (y) and predicted values (ŷ). In other words, residuals tell us how "wrong" our predictions are. We can use this information to evaluate our model's accuracy and make necessary improvements.

## What is a Good Fit for Linear Regression?

A good fit in linear regression means that the data is tightly clustered around the line of best fit. In other words, the closer your observed data points are to your predicted values, the better your regression model fits the data.

## What are the Types of Linear Regression?

There are two types of linear regression. Simple linear regression is used when there is only one independent variable. Multiple linear regression, on the other hand, is used when there are two or more independent variables.

## What are the Assumptions of Linear Regression?

Linear regression makes several assumptions, including:

1. Linearity
2. Homoscedasticity
3. Independence
4. Normality

Violations of these assumptions can negatively impact our model's accuracy.

### References:

1. James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An Introduction to Statistical Learning: with Applications in R.
2. Kutner, M.H., Nachtsheim, C.J., and Neter J.(2004) Applied Linear Regression Models.
3. Vittinghoff E (2012) Regression Methods in Biostatistics.
4. Montgomery D.C., Peck E.A and Vining G.G (2015), Introduction to Linear Regression Analysis.
5. Faraway J.J.(2016), Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models.