Question

What is the purpose of a residual analysis? Which diagrams have to be included. Why? (4 Marks

Answer 1

Residuals

The difference between the observed value of the dependent variable (y) and the predicted value (ŷ) is called the residual (e). Each data point has one residual.

Residual = Observed value - Predicted value
e = y - ŷ

Both the sum and the mean of the residuals are equal to zero. That is, Σ e = 0 and e = 0.

Purpose

A residual plot is a graph that shows the residuals on the vertical axis and the independent variable on the horizontal axis. If the points in a residual plot are randomly dispersed around the horizontal axis, a linear regression model is appropriate for the data; otherwise, a non-linear model is more appropriate.A residual plot is a graph in which residuals are on tthe vertical axis and the independent variable is on the horizontal axis. If the dots are randomly dispersed around the horizontal axis then a linear regression model is appropriate for the data; otherwise, choose a non-linear model.

Types of Residual Plot

Following example shows few patterns in residual plots.

In first case, dots are randomly dispersed. So linear regression model is preferred. In Second and third case, dots are non-randomly dispersed and suggests that a non-linear regression method is preferred.