The linear regression model assumes that there is a straight-line relationship between the predictors and the response. This can be validated by plotting a scatter plot between the features/response and the target/predictor. For example, the scatter plot of the feature TV vs Sales tells us that as the money invested on Tv advertisement increases the sales also increases linearly.


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- Linearity of the response-predictor relations
- Normal distribution of residuals
-  Error terms, e1,e2,...e3, are uncorrelated
-  Error terms have a constant variance
-  Little or no Multicollinearity between the features
-  Homoscedasticity Assumption
-  Large sample size and few or no outliers

Assumptions of Linear Regression

James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An introduction to statistical learning (Vol. 112, pp. 3-7). New York: springer.

An Introduction to Statistical Learning with Applications in R

Homoscedasticity basially means "same variance". So, it is present when the error term is the same across all values of an independent variable. 
Another way to easily understand it - "having the same scatter". 

Homoscedasticity

Linearity of the Response-Predictor Relations

Multicollinearity is a phenomenon in which one variable in a multiple regression model can be linearly predicted from the other variables. This is mostly when the correlation between two independent variables is equal to 1 or −1.

Multicollinearity

This assumption notes that there is no overlapping relationship between error values as it would incorrectly result in reduced error values.

 Error terms, e1, e2,... e3, are uncorrelated

In addition to the assumption of linearity, linear regression typically imposes the assumption that any observation noise is well-behaved and follows a Gaussian (normal) distribution. This means that the deviations of the actual target values from their expected linear values are modeled using a Gaussian probability density function.

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