Homework Assignment

Correlation and Regression

Forecasting is a critical job for managers. Correlation and regression are two statistical methods used by managers for forecasting.

Correlation allows you to quantify how closely two variables are related. The correlation values or correlation coefficients have a range between -1.0 and +1.0. The closer the value is to the absolute value of 1, the stronger the correlation. The negative or positive sign indicates if the variables have a negative or positive correlation. A positive correlation exists when both variables increase or decrease. A negative correlation exists when one variable increases while the other variable decreases. If the two variables are independent and have no relationship, then the correlation is 0.

Be careful not to confuse correlation and causality. For instance, you can be reasonably sure that higher distribution and lower prices both cause higher sales; however, there are many things in this world that are correlated mathematically but are not at all related.

Regression is a statistical technique that lets you construct an equation to describe the relationship between the movements of two variables. On a scatter plot, the regression equation would calculate the best-fit line through the points. Regression allows you to forecast and simulate different scenarios by ascertaining the relationship between causes and effects. The causes are known as independent variables or drivers. The effects are known as dependent variables or what is being forecast.

You need to have a sufficient amount of history for the dependent variable and all the independent variables that you might think are useful in predicting the dependent variable to build a regression model. The minimum number of observations required is generally between 20 and 30. A key concept for regression is that it uses the past to predict the future. It assumes that relationships between historical dependent and independent variables will hold true for present of future dependent and independent variables.

There is an extension to the regression model, known as the multiple regression model. Adding another independent variable to a regression model turns it into a multiple regression model. The equation can become quite complex when more than two independent variables are added to the model, but these equations are rarely calculated by hand. Most commercial spreadsheet, accounting, and statistics software include these in their function library.