Simple Linear Regression in Statistics using Least Squares Method

Simple Linear Regression is a statistical method used to model the relationship between two variables by fitting a linear equation to observed data. The goal is to find the best-fitting straight line through the points in a scatter plot of the data.

???????? my ???????????????? ???????????????? on ???????????????????? & ???????????????? for regular updates: https://whatsapp.com/channel/0029VaAGwzTDJ6H9S5Q4Ow0m

???????? my ???????????????? ???????????????? on ?????????????? ?????????????????? & ?????????????? ?????????????? for regular updates: https://whatsapp.com/channel/0029VaAKJBGKGGGDjcK4mw2h

This line is described by the equation:

?? 75?? ?????????????????????? ???? ?????????????? ??????????????. ?????????????????? ???? ?????????????? ?????????????? : https://www.youtube.com/@DigitalELearning

Least Squares Method

The Least Squares Method is used to find the values of β0 and β1 that minimize the sum of the squared differences between the observed values and the values predicted by the linear model. These differences are called residuals.

In this YouTube video, we will be exploring Simple Linear Regression. We will cover the basic concepts of REGRESSION. We will guide you through the concept of simple linear regression and demonstrate how to perform it using the least squares method with example. So, if you're ready to learn about REGRESSION and how it can help you make sense of your data, then this is the video for you!

?????????????? ???? ???? ?????????????? :

Steps to Perform Simple Linear Regression using Least Squares Method:

• Calculate the Mean of x and y:

• Calculate the Slope (β1):

• Calculate the Intercept (β0\beta_0β0): β0=yˉ?β1xˉ
• Construct the Regression Line: y=β0+β1x

?? ???????????? ???? ???? ??????????????????: https://www.instagram.com/digital_elearning/

Example Calculation

Let's walk through an example with a small dataset:

• Calculate the Means:

• Calculate the Slope (β1\beta_1β1):

• Calculate the Intercept (β0)

• Construct the Regression Line:

y=1.3+0.9x

This line represents the best fit for the given data using the least squares method.

?????????????? ???? ?????? ?????????? ???????????????? ??????????????: https://www.whatsapp.com/channel/0029VaEWKWbIiRovZpAduc0p

?????????????? ???? ???????? ?????? ?????????? ???????????????? ??????????????: https://www.whatsapp.com/channel/0029VaAUuqs4inooet3e4S3O

?????????????? ???? ?????????????? ???????????????????? ???????????????? ??????????????:

https://www.whatsapp.com/channel/0029Va8slQdEAKWAhXoQK13B

?????????????? ???? ?????????????? ?????????????????? & ?????????????? ?????????????? ???????????????? ??????????????:

https://www.whatsapp.com/channel/0029VaAKJBGKGGGDjcK4mw2h

Summary

The simple linear regression equation y=1.3+0.9xy = 1.3 + 0.9xy=1.3+0.9x can now be used to predict the value of yyy for any given xxx. This method helps to understand and predict the relationship between the two variables.