# What are the differences between the linear regression and multiple linear regression?

I'm interested to know that, what is the difference between linear regression and multiple linear regression? both of them seems same to me.

• Linear regression might have one x-variable (simple linear regression) or more than one. Multiple linear regression can only refer to the case where there's more than one. – Glen_b -Reinstate Monica Jan 29 '14 at 14:27
• @Glen_b, I didn't exactly get it. you say that Linear regression might have one x-variable or more than one. Multiple linear regression can only more than one x-variable ? – user2806363 Jan 29 '14 at 14:36
• Correct. Linear regression can encompass both simple- and multiple- linear regression (though perhaps more frequently refers to simple linear regression). But those latter two terms are mutually exclusive categories. – Glen_b -Reinstate Monica Jan 29 '14 at 14:40

By linear regression I assume that you mean simple linear regression. The difference is in the number of independent explanatory variables you use to model your dependent variable.

Simple linear regression

$Y=\beta X+\beta_0$

Multiple linear regression

$Y=\beta_1 X_1+\beta_2 X_2+...+ \beta_m X_m + \beta_0$

Where the $\beta$'s are the parameters to fit. In other words simple linear regression is just a special case of multiple linear regression.

This is not the same as multivariate linear regression which has more than one dependent variable.

• Why list the intercepts last? It's ... rather unconventional. – Glen_b -Reinstate Monica Jan 29 '14 at 14:25
• That's just the way I've always written it. I guess it's just my preference. The order in which one is writing it is of course irrelevant. Feel free to change it if you believe it enhances the clarity and readability of the answer. – Dr. Mike Jan 29 '14 at 14:31
• Actually, I am okay with preference as a reason. I guess highlighting it (as we've just done) is probably sufficient. – Glen_b -Reinstate Monica Jan 29 '14 at 14:36
• @Glen_b: and oddly, it would be conventional if written as $y = ax + b$. – Cliff AB May 26 '16 at 4:58