# Simple Linear Regression Model Solved Example

## Simple Linear Regression Model Solved Example in Machine Learning

Regression modeling is a process of determining a relationship between one or more independent variables and one dependent or output variable.

Example:

1. Predicting the height of a person given the age of the person.

2. Predicting the price of the car given the car model, year of manufacturing, mileage, engine capacity.

### Simple Linear Regression Model

Assume that there is only one independent variable x. If the relationship between x (independent variable) and y (dependent or output variable) is modeled by the relation,

y = a + bx

then the regression model is called a linear regression model.

### Problem Deninition:

Find a quadratic regression model for the following data:

### Solution:

Let the simple linear regression model be

y = a + bx

### Steps to find a and b,

First, find the mean and covariance.

Means of x and y are given by,

The variance of x is given by,

The covariance of x and y, denoted by Cov(x, y)is defined as,

Now the values of a and b can be computed using the following formulas:

First, find the mean of x and y,

Next, find the Covariance between x and y,

Now find the variance of x,

Now, find the intercept and coefficients,

Therefore, the linear regression model for the data is,

### Summary

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