# Regression

Regression is a statistical tool for quantifying a model. The key output of regression is a formula, such as:

`$Sales = $121 + 4.1 × $TV Advertising Expenditure + 3.2 × $Online Advertising Expenditure `

With such a formula it is possible to:

- Make
*predictions*. For example, using the formula above, a firm that spends $1,000,000 on TV advertising and nothing on advertising expenditure is predicted to have sales of $121 + 4.1 × $1,000,000 = $4,100,121. - Draw conclusions about
*relative*effectiveness. For example, the equation above shows that TV advertising is more effective than online advertising.

Most regression models are characterized by having one *dependent variable* and one or more *independent variables*.

In the example above the dependent variable is sales. Common dependent variables in survey analysis applications of regression include:

- Overall satisfaction with a product or a service.
- Likelihood to recommend a product or service.
- Net Promoter Score.
- Likelihood to use a product or service again.
- Product quality.
- Frequency of buying or using a product or service.

The *independent variables* will typically be a list of variables that are believed to determine the value of the dependent variable. In the example above, the independent variables are `$TV Advertising Expenditure`$Online Advertising Expenditure</tt>. In most applications of regression to survey analysis, the independent variables are either:

- Demographic variables. For example, if wishing to identify high value customers, the dependent variable may be amount of money spent and the independent variables would be demographics.
- Measurements of performance in different areas. For example, if the dependent variable measures satisfaction with an airline the independent variables could be things such as satisfaction with the food, satisfaction with the cabin crew, satisfaction with the in-flight entertainment, and so on. Such a regression model is known as a
*driver analysis*. - Measurements of effort in different areas. For example, expenditures on different types of advertising, such as in the above example.