2. The key difference between simple and multiple regression is: Simple regression assumes a linear relationship between variables whereas this assumption is not necessary for multiple regression. Multiple linear regression introduces polynomial features. Simple linear regression compresses multidimensional space into one dimension. To estimate a single dependent variable, simple regression uses one independent variable whereas multiple regression uses multiple.

The key difference between simple and multiple regression is:<br /><br />To estimate a single dependent variable, simple regression uses one independent variable whereas multiple regression uses multiple.<br /><br />In simple linear regression, the goal is to model the relationship between a single independent variable and a dependent variable. The equation for simple linear regression is:<br /><br />y = β0 + β1x + ε<br /><br />where y is the dependent variable, x is the independent variable, β0 is the intercept, β1 is the slope, and ε is the error term.<br /><br />In multiple linear regression, the goal is to model the relationship between a dependent variable and multiple independent variables. The equation for multiple linear regression is:<br /><br />y = β0 + β1x1 + β2x2 +... + βnxn + ε<br /><br />where y is the dependent variable, x1, x2,..., xn are the independent variables, β0 is the intercept, β1, β2,..., βn are the coefficients, and ε is the error term.<br /><br />The key difference is that multiple regression uses multiple independent variables to estimate the dependent variable, whereas simple regression uses only one independent variable.