List all assumptions for data to be met before starting with linear regression

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Before starting linear regression, the assumptions to be met are as follow:

  • Linear relationship
  • Multivariate normality
  • No or little multicollinearity
  • No auto-correlation
  • Homoscedasticity

Before applying linear regression, it’s important to ensure that certain assumptions about the data are met to obtain reliable results. Here are the key assumptions:

  1. Linearity: The relationship between the independent variables (features) and the dependent variable (target) should be linear. This means that changes in the independent variables result in proportional changes in the dependent variable.
  2. Independence: Observations in the dataset should be independent of each other. This means that there should be no correlation between the residuals (errors) of the model. Independence ensures that each observation provides new information to the model.
  3. Homoscedasticity: The variance of the residuals should be constant across all levels of the independent variables. In other words, the spread of the residuals should remain uniform as the values of the independent variables change. This ensures that the model’s predictions are equally accurate across the range of observed values.
  4. Normality of Residuals: The residuals should follow a normal distribution. This means that the distribution of the errors should be approximately symmetric around zero. Normality ensures that the estimates of the model parameters are unbiased and that the confidence intervals and hypothesis tests are valid.
  5. No Multicollinearity: There should be no high correlation between independent variables. Multicollinearity can lead to unstable estimates of the regression coefficients, making it difficult to interpret the effects of individual predictors on the target variable.
  6. No Autocorrelation: There should be no correlation between the residuals at different time points (for time series data) or different observations (for cross-sectional data). Autocorrelation indicates that there is some pattern left in the residuals, which violates the assumption of independence.

Ensuring these assumptions are met or appropriately addressed (e.g., through data transformations or model adjustments) is crucial for the reliability and interpretability of the results obtained from linear regression analysis.