Statistics for Business: Decision Making and Analysis, 3rd Edition

... sequence is often called a data-generating process. The data-generating process is particularly important in regression analysis because of the distinct roles of the explanatory variable and response. The model describes the conditional average of the response given the explanatory variable, not the other way around.

As an illustration, let Y denote monthly sales of a company and let X denote its spending on advertising (both scaled in thousands of dollars). To specify the SRM, we assign values to the three parameters β₀, β₁, and σ_ε. Suppose that β₀ = 500 and β₁ = 2; if the company spends x thousand dollars on advertising, then the conditional mean of sales in thousands of dollars is

$${\mu }_{y|x}=500+2x$$

Without advertising (x = 0), β₀ indicates that sales average ...