Simple linear regression uses one independent variable to predict a dependent variable and finds the linear relationship between them as y = b0 + b1*x1, where b0 is the y-intercept and b1 is the slope. Multiple linear regression expands on this by using multiple independent variables to predict the dependent variable according to the equation y = b0 + b1*x1 + b2*x2 + ... + bn*xn, where there are coefficients for each independent variable that contribute to predicting y. Both types of regression analyze the linear relationships between variables.