# Simple Linear Regression Models and the Math Behind Them.

A linear regression model establishes a linear relationship between the dependent and independent variables in a model. *So what exactly do i mean by the dependent and independent variables?*

Suppose you were establishing the relationship between the number of years of experience and the salary someone should earn. The graph would look something like this:

As you can see, the more experienced someone is, the more they earn(according to the chart above).

In this case, the salary will depend on the experience level. ** The salary is therefore the dependent variable(its depending on something) and the experience will be the independent variable**.

Another way to think of it is: The dependent variable is what is being influenced/what we are trying to predict and the independent variable is what is influencing it.

Another question would be: What is the math behind this model?

Assuming you did some high school math, the equation of a linear graph is:

**Y = MX + C**

If i match that to the salary vs experience graph,

Y - Salary (Target/dependent variable)

M- The slope/coefficient of the graph. This will also tell us what kind of relationship to expect. If it is a positive number, then the dependent variable will increase as the independent value increases. If it is a negative value, then as the value of one increases, the value of the other decreases.

X- the experience (Independent variable)

C- The intercept value. This is where the line will cross the Y-Axis.

As you also can note, the line graph does not necessarily touch all the data points(in blue). **The line generated, known as the linear regression line is known as the line of best fit.**

In layman's terms, this is a straight line that gives the best approximation of the data set.

A rough way of estimating this would be to draw a straight line through as many points as possible, so that the number of data points above and below the line are somewhat equal.

**This can however also be mathematically calculated using the least squared method. An explanation can be found here:**

Now, suppose the task was to establish how much someone who has 3.5 years of experience should earn:

All you need to do is draw a straight line to meet the line and the corresponding salary value will be the salary value. This is the whole idea behind a linear model.

As an example I have created a repository for a beginner Linear Regression model on my GitHub. https://github.com/AbigaelN2021/AndelaLearningCommunity/tree/main/LinearRegression