Question

What is the difference between simple and multiple regression and what is the equation like?

A) Simple uses one independent variable; Multiple uses multiple independent variables; Equation is Y = b0 + b1X
B) Simple uses multiple independent variables; Multiple uses one independent variable; Equation is Y = b0 + b1X1 + b2X2
C) Both use only one independent variable; Equation is Y = b0 + b1X
D) Both use multiple independent variables; Equation is Y = b0 + b1X1 + b2X2

Answer 1

Simple regression uses one independent variable and the equation is Y = b0 + b1X, while multiple regression uses multiple independent variables and has an equation like Y = b0 + b1X1 + b2X2 + ... + bnXn. The correct choice from the options given is A.

Step-by-step explanation:

The difference between simple and multiple regression is primarily based on the number of independent variables they use. Simple regression includes only one independent variable, while multiple regression involves two or more independent variables. Correspondingly, the equation for simple linear regression is Y = b0 + b1X, where Y is the dependent variable, b0 is the y-intercept, b1 is the slope, and X is the one independent variable. On the other hand, the equation for multiple regression is in the form of Y = b0 + b1X1 + b2X2 + ... + bnXn, which extends the simple linear regression equation by adding more terms, each with their own coefficient, for each additional independent variable.

Based on the options provided and relating to the concepts of linear equations, the correct answer would be option A: Simple uses one independent variable; Multiple uses multiple independent variables; Equation is Y = b0 + b1X.