| **Causal Forecast - Sales and Advertising Investments** | **View ** |

Description: Causal Forecasting (using Linear Regression Analysis)

This example shows show how linear regression analysis can be used to create a causal forecast. Regression analysis is one of the most widely used techniques for analyzing historical or experimental data. It is often considered a causal forecasting method. In short, regression lets you determine to what extent a measured result is correlated to input values.

Example:

Assume a company wants to use historical data to assess the effectiveness of magazine, newspaper, and TV advertising for a brand of laundry detergent. In the past eight quarters the company recorded total sales and advertising expenditures in three mediums.

You want to know if there is any relationship between advertising and sales; and if so, which type of advertising seems to be most effective. To solve this problem, you use your historical data (shown in the Data table). Then using the Regression option in the Tools menu, a regression analysis is performed, the results of which are shown in the Regression Statistics table.

The results mean that you could write a mathematical equation relating Sales and your investments in Magazine, Newspaper, and TV. In this example, the equation is:

Sales = 956.14 + 1.25 Magazine + 0.92 Newspaper + 3.52 TV

In other words, TV advertising seems to contribute the most to sales at $3.52 per $1 of advertising.

However, you must check the standard error of these coefficients before you can conclude that there is any significant correlation between advertising and sales at all. The coefficient for magazine advertising has a standard error of 0.81 compared to a coefficient value of 1.25. Since the standard error is large compared to the coefficient value, you cannot conclude that there is any correlation between magazine advertising and sales.

As a rule, the coefficient should be about twice as large as the corresponding standard error before any correlation can be assumed. The T-statistic is the standard error divided by the coefficient value for each input. Therefore, a T-statistic greater than two is an indication of strong correlation. The only T-statistic greater than two is the one for TV advertising. This means that there is a statistically significant correlation between TV advertising and sales in the historical data.

The R Squared value is a measure of how well the linear model fits the actual sales data. The value 0.79 means that 79% of the variance in sales is explained by changes in the three advertising categories.

Author: Vanguard Software