## What Is a Statistical Relation

deterministic relation

Relation known with certainty statistical relation

Inexact relation time series

Daily, weekly, monthly or annual sequence of data cross section

Data from a common point in time scatter diagram

### Plot of XY data

To understand when the use of regression analysis is appropriate, one must appreciate a basic difference between two broad classes of economic relations.

A deterministic relation is one that is known with certainty. For example, total profit equals total revenue minus total cost, or n = TR - TC. Once the levels of total revenue and total cost are known with certainty, total profits can be exactly determined. The profit relation is an example of a deterministic relation. If total cost = \$5 X quantity, then total cost can be exactly determined once the level of quantity is known, just as quantity can be determined once the total cost level is known. If all economic relations were deterministic, then managers would never be surprised by higher or lower than expected profits; total revenues and total costs could be exactly determined at the start of every planning period. As it turns out, few economic relations are deterministic in nature. It is far more common that economic variables are related to each other in ways that cannot be predicted with absolute accuracy. Almost all economic relations must be estimated.

A statistical relation exists between two economic variables if the average of one is related to another, but it is impossible to predict with certainty the value of one based on the value of another. In the earlier example, if TC = \$5Q on average, then a one-unit increase in quantity would tend to result in an average \$5 increase in total cost. Sometimes the actual increase in total cost would be more than \$5; sometimes it would be less. In such circumstances, a statistical relation exists between total costs and output.

When a statistical relation exists, the exact or "true" relation between two economic variables is not known with certainty and must be estimated. Perhaps the most common means for doing so is to gather and analyze historical data on the economic variables of interest. A time series of data is a daily, weekly, monthly, or annual sequence of data on an economic variable such as price, income, cost, or revenue. To judge the trend in profitability over time, a firm would analyze the time series of profit numbers. A cross section of data is a group of observations on an important economic variable at any point in time. If a firm were interested in learning the relative importance of market share versus advertising as determinants of profitability, it might analyze a cross section of profit, advertising, and market share data for a variety of regional or local markets. To assess the effectiveness of a quality management program, the firm might consider both time-series and cross-section data.

The simplest and most common means for analyzing a sample of historical data is to plot and visually study the data. A scatter diagram is a plot of data where the dependent variable is plotted on the vertical or Y-axis, and the independent variable is plotted on the horizontal or X-axis. Figure 3.3 shows scatter diagrams that plot the relation between four different unit cost 