linear regression !!!

 

Linear Regression

Definition: Linear regression is a statistical method used to model the relationship between a dependent variable (outcome) and one or more independent variables (predictors). The goal is to find the best-fitting line that describes how the dependent variable changes as the independent variable(s) change.

Key Components:

1. Dependent Variable (Y): The outcome we are trying to predict.

2. Independent Variable(s) (X): The predictors used to make predictions about Y.

3. Equation of the Line: The linear regression model is typically expressed as:

   $$Y = b_0 + b_1X_1 + b_2X_2 + ... + b_nX_n + \epsilon$$

   where $b_0$ is the intercept, $b_1, b_2, ..., b_n$ are the coefficients, and $\epsilon$ represents the error term.

4. Assumptions:

   • Linearity: The relationship between the dependent and independent variables is linear.
   • Independence: Observations are independent of one another.
   • Homoscedasticity: The variance of errors is constant across all levels of the independent variables.
   • Normality: The residuals (errors) should be normally distributed.

5. Goodness of Fit: Measured by $R^2$, which indicates the proportion of variance in the dependent variable explained by the independent variables. Values range from 0 to 1, with higher values indicating a better fit.

6. Statistical Significance: The significance of the coefficients is typically tested using t-tests, and the overall model fit is tested using an F-test.

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