Simple Linear Regression Model Solved Example

 
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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:

XY
11
22
31.3
43.75
52.25

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,

Mean

The variance of x is given by,

variance

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

Covariance

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

a and b in linear regression

First, find the mean of x and y,

mean and x and y

Next, find the Covariance between x and y,

Covariance
Covariance 1

Now find the variance of x,

Variance
Variance 1

Now, find the intercept and coefficients,

intercept and coefficients
intercept and coefficients 1

Therefore, the linear regression model for the data is,

Linear regression model

Video Tutorial – Simple Linear Regression Model

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