The MBA Math Monday series helps prospective MBA students to self assess their proficiency with the quantitative building blocks of the MBA first year curriculum.
Linear regression helps to identify the best line characterizing two sets of data. Regression generally is used where one factor managers control, such as advertising, is believed to influence another factor of interest, such as sales. The notion of causality can be wrong, however, so like much of statistics it is important to understand the tool and use it wisely. Linear regression also quantifies the degree of linearity in a relationship, which you can see in a scatterplot by the extent to which the data create a line versus a scattered set of dots.
Various nonlinear regression options are available at the click of a button in Excel, all with risks of incorrect assumptions and unwise overprecision.
One need only look at the monumental financial consequences of failure to anticipate the end of rising house prices to understand that extrapolating the past blindly into the future can be disastrous. Understanding linear regression is an important step in absorbing the value and limits of statistics.
Exercise:
Consider the following sample data for the relationship between advertising budget and sales for Product A:
| Observation | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Advertising ($K) | 60 | 70 | 70 | 80 | 80 | 90 | 100 | 100 | 100 | 110 |
| Sales ($K) | 362 | 416 | 417 | 499 | 485 | 536 | 602 | 623 | 616 | 663 |
What is the slope of the “least-squares” best-fit regression line?
Solution (with audio commentary): click here
Prof. Peter Regan created the self-paced, online MBA Math quantitative skills course and teaches live MBA courses at Dartmouth (Tuck), Duke (Fuqua), and Cornell (Johnson).