# Linear Regression in R

Regression analysis is a very widely used statistical tool to establish a relationship model between two variables. One of these variables is called **predictor **variable whose value is gathered through experiments. The other variable is called **response **variable whose value is derived from the predictor variable.

In Linear Regression these two variables are related through an equation, where **exponent **(power) of both these variables is 1. Mathematically a linear relationship represents a **straight line** when plotted as a graph. A non-linear relationship where the exponent of any variable is not equal to 1 creates a curve.

The general mathematical equation for a linear regression is:

y = ax+b

Following is the description of the parameters used:

**y**is the response variable.**x**is the predictor variable.

**a** and b are constants which are called the coefficients.

**Input Data**

Below is the sample data representing the observations:

# Values of height

151, 174, 138, 186, 128, 136, 179, 163, 152, 131

# Values of weight.

63, 81, 56, 91, 47, 57, 76, 72, 62, 48

**lm() Function**

This function creates the relationship model between the predictor and the response variable.

**Syntax **

The basic syntax for **lm()** function in linear regression is:

**lm(formula,data) **

Following is the description of the parameters used:

**formula**is a symbol representing the relation between x and y.

**data** is the vector on which the formula will be applied.

x <- c(151, 174, 138, 186, 128, 136, 179, 163, 152, 131)

y <- c(63, 81, 56, 91, 47, 57, 76, 72, 62, 48)

relation <- lm(y~x)

print(relation)

# Find weight of a person with height 170.

a <- data.frame(x=170)

result <- predict(relation,a)

print(result)