Assumptions

1. Independence: Observations should be independent of each other. In other words, the value of the dependent variable for one observation should not be influenced by the values of the other observations
2. Linearity: The relationship between the independent and dependent variables is assumed to be linear.
3. No Perfect Multicollinearity: Independent variables are not correlated with each other. There can’t be a linear relationship between a variable and a group of variables
4. Normality of Residuals: Residuals are assumed to be normally distributed. This assumption is important for hypothesis testing and confidence interval estimation.
5. Homoscedasticity: Residuals have constant variance across all values of the independent variables.
6. No Autocorrelation of Residuals: Residuals do not exhibit patterns or correlations over time. Residuals are independent of each other

Consequences of Violation

1. Independence: Biased standard errors affecting the reliability of hypothesis tests and confidence intervals
2. Linearity: Coefficients are not accurately estimated, thus inaccurate predictions
3. No Perfect Multicollinearity: Imprecise coefficient estimates
4. Normality of Residuals: Accuracy of hypothesis tests and confidence intervals impacted

Detection

1. Independence

2. Linearity

Scatter plots