Linear Regression: Simple Steps, Video. Find Equation, Coefficient, Slope

“Linear” means line. The word Regression came from a 19th-Century Scientist, Sir Francis Galton, who coined the term “regression toward mediocrity” (in modern language, that’s regression to the mean. He used the term to describe the phenomenon of how nature tends to dampen excess physical traits from generation to generation (like extreme height).

Why use Linear Relationships?

Linear relationships, i.e. lines, are easier to work with and most phenomenon are naturally linearly related. If variables aren’t linearly related, then some math can transform that relationship into a linear one, so that it’s easier for the researcher (i.e. you) to understand.

What is Simple Linear Regression?

You’re probably familiar with plotting line graphs with one X axis and one Y axis. The X variable is sometimes called the independent variable and the Y variable is called the dependent variable. Simple linear regression plots one independent variable X against one dependent variable Y. Technically, in regression analysis, the independent variable is usually called the predictor variable and the dependent variable is called the criterion variable. However, many people just call them the independent and dependent variables. More advanced regression techniques (like multiple regression) use multiple independent variables.

Regression analysis can result in linear or nonlinear graphs. A linear regression is where the relationships between your variables can be described with a straight line. Non-linear regressions produce curved lines

Regression analysis is almost always performed by a computer program, as the equations are extremely time-consuming to perform by hand.

What is Simple Linear Regression?

If you’re just beginning to learn about regression analysis, a simple linear is the first type of regression you’ll come across in a stats class.

Linear regression is the most widely used statistical technique; it is a way to model a relationship between two sets of variables. The result is a linear regression equation that can be used to make predictions about data. 

How to Find a Linear Regression Equation: Overview

Regression analysis is used to find equations that fit data. Once we have the regression equation, we can use the model to make predictions. One type of regression analysis is linear analysis. When a correlation coefficient shows that data is likely to be able to predict future outcomes and a scatter plot of the data appears to form a straight line, you can use simple linear regression to find a predictive function. If you recall from elementary algebra, the equation for a line is y = mx + b. This article shows you how to take data, calculate linear regression, and find the equation y’ = a + bx. Note: If you’re taking AP statistics, you may see the equation written as b0 + b1x, which is the same thing (you’re just using the variables b0 + b1 instead of a + b

The Linear Regression Equation

Linear regression is a way to model the relationship between two variables. You might also recognize the equation as the slope formula. The equation has the form Y= a + bX, where Y is the dependent variable (that’s the variable that goes on the Y axis), X is the independent variable (i.e. it is plotted on the X axis), b is the slope of the line and a is the y-intercept.

The first step in finding a linear regression equation is to determine if there is a relationship between the two variables. This is often a judgment call for the researcher. You’ll also need a list of your data in x-y format (i.e. two columns of data—independent and dependent variables).

How Do Simple Linear Regression Using SPSS

How Do Multiple Linear Regression Using SPSS