6.2 Linear Regression and Extensions

Suppose that you want to find if the relationship between a single independent variable, X (e.g., Year), and a dependent variable, Y (e.g., Sales), can be closely represented by a straight line. The method of least squares can be used to compute an intercept and a slope to give an equation of the form

where b is the estimated intercept, k is the estimated slope, and e is the error between the true value of Y and the value predicted by (b + kX). It is important to understand that no cause-and-effect relationship has been posited between X and Y. You are merely studying an ongoing association between the two. This is sometimes called naive modeling, as opposed to causal modeling.

Exhibit 6.1 Applying the Excel Trend Macro to RFID Sales

MS Excel spreadsheet software has been used for this case study. For example, suppose you have the number of passive RFID tags sold over the past several years (Table 6.3). These are not actual data; they are used only as an example.

Year | Passive Tags Sold (millions) |

2003 | 18 |

2004 | 40 |

2005 | 91 |

2006 | 150 |

2007 | 275 |

2008 | 413 |

As Figure 6.5 shows, a straight line provides a pretty good fit to those data. How should you fit such a line? You could use a straightedge and then calculate the slope and intercept. Or you could use MS Excel (for instance) to perform a linear regression (the “LINEST” ...

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