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Assumption of Linear regression makes several key assumptions:

1. Linearity: The relationship between the independent variable(s) and the dependent variable is assumed to be linear.

2. Independence: The residuals (the differences between observed and predicted values) should be independent of each other. In other words, the value of the dependent variable for one observation should not predict the value of the dependent variable for another observation.

3. Homoscedasticity: The variance of the residuals should be constant across all levels of the independent variable(s). This implies that the spread of the residuals should be roughly the same for all values of the independent variable.

4. Normality of residuals: The residuals should follow a normal distribution. This assumption is not crucial for large sample sizes due to the Central Limit Theorem, but it can be important for smaller sample sizes.

5. No perfect multicollinearity: In multiple regression, the independent variables should not be perfectly correlated with each other. This means that one independent variable should not be a perfect linear function of another.

These assumptions are essential for the validity and reliability of the linear regression model. Violations of these assumptions might lead to biased or inefficient estimates.

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