Assumptions of Linear Regression

Assumptions of Linear Regression: In order for the results of the regression analysis to be interpreted meaningfully, certain conditions must be met:
1) Linearity: There must be a linear relationship between the dependent and independent variables.
2) Homoscedasticity: The residuals must have a constant variance.
3) Normality: The residuals must be normally distributed.
4) No Multicollinearity: No high correlation between the independent variables

Linearity:
In linear regression, a straight line is placed through the data. This straight line should represent all points as good as possible. If the relation is nonlinear the straight line cannot fulfill this requirement.

Normal distribution of the error:
One assumption of linear Regression is that the error epsilon must be normally distributed,
To check this there are two ways, one is the analytical way and the other is the graphical way.

Homoscedasticity:
A assumption for linear regression is that the residuals have a constant variance.
Since your regression model never exactly predicts your dependent variable in practice, you always have an error. Now you can plot your dependent variable on the x axis and the error on the y axis.

Multicollinearity:
In multicollinearity, two or more of the predictors correlate strongly with each other.

Test your assumptions for the linear Regression online:

And here are mor informations about Regression:

[KitsGravity]

Well explained. Thanks for including the diagnostics, which is by far the most important part and something not often covered in most of the videos.

[MuhammadAnas-ctom]

Fantastic explanation. Presentation of the concept is excellent

[shubhamthote]

Hello Ma'am, your teaching technique really Awesome.
Please make a video lecture on
""" What if these Linear Regression Assumption get violated ? """

[ishaqhussain]

Presentation of the concept is excellent 👍.

Much appreciated 🎉

[perpalmgren]

Hi! Thank you for a great statistic program and wonderful tutorials.
One question and one statement:
- Why are not two other important assumptions addressed, namely the problem with outliers and the requirement if independence of residuals?
- Maybe it should be better illuminated that normality refers to that it is the residuals that should be normally distributed about the predicted dependents variables sore. It can be misunderstood that it is the raw data that should be normally distributed.

[devanshujindal]

Thank you ma'am for such a simple explanation it really helped me

[car]

so wtf do i do if my data isnt linear? just show a graph saying its not linear therefore i havent bothered to run and stats and all these data and research is a waste of time ?

[marwatawfik]

Thanks so much.
Do you have some features open (free) for students (i.e. regression)?

[alia]

Thanks so much. What about the assumption: independence of the observations?

[retenim]

Hi, thanks for the video. Regarding the second assumption (residuals must be normally distributed). Does the histogram represent the normal distribution of the residual, right? I didn't understand if the points in the qqplot are the residuals or the sample data

[bhavaniprasadraoejanthkar]

Hey! Your videos are awesome! It would be great if you make more videos on Machine Learning concepts.

[Gesuselsaviour]

Thanks for the video, found it very helpful. Do we also have to ensure that there are no influential points in the data?

[zimalkhan]

Some segments in the video are stamped not adjacent to each other