**Variables**

At the center of regression is the relationship between two variables, called the dependent and independent variables. For instance, suppose you want to forecast sales for your company and you've concluded that your company's sales go up and down depending on changes in GDP. The sales you are forecasting would be the dependent variable because their value "depends" on the value of GDP, and the GDP would be the independent variable. You would then need to determine the strength of the relationship between these two variables in order to forecast sales. If GDP increases/decreases by 1%, how much will your sales increase or decrease?

**Covariance**

**Correlation Coefficient****Regression Equation**

Now that we know how the relative relationship between the two variables is calculated, we can develop a regression equation to forecast or predict the variable we desire. Below is the formula for a simple linear regression. The "y" is the value we are trying to forecast, the "b" is the slope of the regression, the "x" is the value of our independent value, and the "a" represents the y-intercept. The regression equation simply describes the relationship between the dependent variable (y) and the independent variable (x).

Figure 1: Line of best fit |

Source: Investopedia, 2009. |

**Excel**

Now that you understand some of the background that goes into regression analysis, let's do a simple example using Excel's regression tools. We'll build on the previous example of trying to forecast next year's sales based on changes in GDP. The next table lists some artificial data points, but these numbers can be easily accessible in real life.

Year | Sales | GDP |

2005 | 100 | 1.00% |

2006 | 250 | 1.90% |

2007 | 275 | 2.40% |

2008 | 200 | 2.60% |

2009 | 300 | 2.90% |

*Tools*drop-down menu, select

*Data Analysis*, and from there choose

*Regression*. The popup box is easy to fill in from there; your Input Y Range is your "Sales" column and your Input X Range is the change in GDP column; choose the output range for where you want the data to show up on your spreadsheet and press OK. You should see something similar to what is given in the table below

Regression Statistics | Coefficients | ||

Multiple R | 0.8292243 | Intercept | 34.58409 |

R Square | 0.687613 | GDP | 88.15552 |

Adjusted R Square | 0.583484 | - | - |

Standard Error | 51.021807 | - | - |

Observations | 5 | - | - |

**Interpretation**

The major outputs you need to be concerned about for simple linear regression are the R-squared, the intercept and the GDP coefficient. The R-squared number in this example is 68.7% - this shows how well our model predicts or forecasts the future sales. Next we have an intercept of 34.58, which tells us that if the change in GDP was forecasted to be zero, our sales would be about 35 units. And lastly, the GDP correlation coefficient of 88.15 tells us that if GDP increases by 1%, sales will likely go up by about 88 units.

So how would you use this simple model in your business? Well if your research leads you to believe that the next GDP change will be a certain percentage, you can plug that percentage into the model and generate a sales forecast. This can help you develop a more objective plan and budget for the upcoming year. Of course this is just a simple regression and there are models that you can build that use several independent variables called multiple linear regressions. But multiple linear regressions are more complicated and have several issues that would need another article to discuss.