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linear regression - Coggle Diagram

- - - - Simple Linear regression is a linear regression technique which plots a straight line within data points to minimise error between the line and the data points. It is one of the most simple and basic types of machine learning regression. The relationship between the independent and dependent variables is assumed to be linear in this case. This approach is simple because it is used to explore the relationship between the dependent variable and one independent variable. Outliers may be a common occurrence in simple linear regression because of the straight line of best fit.
    - - Simple linear regression is used to estimate the relationship between two quantitative variables
    - - How strong the relationship is between two variables
    - - Simple linear regression formula
        
        The formula for a simple linear regression is:
        
        y : is the predicted value of the dependent variable (y) for any given value of the independent variable (x).
        B0 : is the intercept, the predicted value of y when the x is 0.
        B1 : is the regression coefficient – how much we expect y to change as x increases.
        x : is the independent variable ( the variable we expect is influencing y).
        e : is the error of the estimate, or how much variation there is in our estimate of the regression coefficient.
        Linear regression finds the line of best fit line through your data by searching for the regression coefficient (B1) that minimizes the total error (e) of the model.
  - - - Multiple linear regression is a technique used when more than one independent variable is used. Polynomial regression is an example of a multiple linear regression technique. It is a type of multiple linear regression, used when there is more than one independent variable. It achieves a better fit in the comparison to simple linear regression when multiple independent variables are involved. The result when plotted on two dimensions would be a curved line fitted to the data points.
    - - You can use multiple linear regression when you want to know: How strong the relationship is between two or more independent variables and one dependent variable
    - - multiple linear regression is used to estimate the relationship between two or more independent variables and one dependent variable.
    - - The formula for a multiple linear regression is:
        
        yi : is the dependent or predicted variable
        β0 : is the y-intercept, i.e., the value of y when both xi and x2 are 0.
        
        β1 and β2 : are the regression coefficients representing the change in y relative to a one-unit change in xi1 and xi2, respectively.
        
        βp : is the slope coefficient for each independent variable
        
        ϵ : is the model’s random error (residual) term.