Appendix II. Basics of Multiple Regression

• Pages: 397-414

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APPENDIX II

THE BASICS OF MULTIPLE REGRESSION

A. Introduction

This appendix illustrates, through examples, the basics of multiple

regression analysis in legal proceedings.

B. Correlation Between Two Variables

Often, visual displays are helpful to describe the relationship

between variables that are used in multiple regression analysis. Consider

a market in which sellers bid to supply a product to purchasers. Figure 1

is a scatterplot that relates the price (P) for Product G (shown on the y, or

vertical, axis) and number of bidders (Bidders, shown on the x, or

horizontal, axis). Each point on the scatterplot shows the contract price

paid for a standard quantity of Product G sold in a bidding contest and

the number of bidders in the contest. For example, in the contest

represented by Point A in Figure 1, the Product G was sold for $200 and

there were five bidders.

The linear relationship between two variables can be summarized by

a correlation coefficient, 1 which ranges in value from –1 (a perfect

negative relationship) to +1 (a perfect positive relationship).

There are at least three possible linear relationships between the

number of bidders and P. In Figure 1, there is a positive correlation. In

general, more bidders are associated with higher prices for Product G,

and fewer bidders are associated with lower prices.

1. Correlation coefficients also frequently are used to discuss the correlation

between the right-hand-side, or independent, variables.

Econometrics in Antitrust

398

Figure 1

Positive Correlation

Price

Bidders

1

5

$100

$200

A

In Figure 2, the correlation is negative: fewer bidders are associated

with higher prices, and lower prices are associated with more bidders.

Figure 2

Negative Correlation

Price

Bidders

1

5

$100

$200