What is Regression? What is B? What is E? What are the regression coefficients?

With regression we strive to find the line that best describes the data collected, then estimate the gradient and intercept of the line. Having defined these values, we can insert different values of our predictor variable into the model to estimate the value of the outcome variable or dependent variable.

A line that has a gradient with a positive value describes a positive relationship

A line that has a negative gradient describes a negative relationship

A thicker line describes a positive relationship

A thinner line describes a negative relationship

In regression analysis we fit a predictive model to our data and use that model to predict values of the dependent variable (DV) from one or more independent variables (IVs)

Simple regression is predicting an outcome variable from a single predictor variable

Multiple regression is predicting an outcome from several predictor variables

This is an incredibly useful tool because it allows us to go a step beyond the data that we actually process.

We can predict any data using the following general equation:
Outcome i = (Model i) + error i

In regression the model we fit is a linear model based on a straight line
In the equation the model gets replaced by some things that define the line that we fit to the data. Any straight line can be defined by 2 things (1) the slope or gradient of the line usually denoted by b 1) and (2) the point at which the line crosses the vertical axis of the graph (known as the intercept of the line, b2)

The general model becomes

Yi = (b0 + b1 Xi) + Ei

Yi = the outcome that we want to predict

Xi = is the ith participant’s score on the predicator variable

b1 = the gradient of the straight line fitted to the data

b0 = the intercept of the line

Ei = represents the difference between the score predicted by the line for participant i and the score that participant i actually obtained. This term represents the fact that the model will not fit perfectly to the data collected.

These parameters b1 and b0 are known as the regression coefficients and generally referred to as B or Bi meaning B associated with the variable i.

Leave a Comment

Your email address will not be published. Required fields are marked *

Skip to content