1.2 Statistical and deterministic relationships

A relationship such as \(F = \frac 95 C + 32\) between temperatures in Fahrenheit and Celsius is deterministic: given \(C\), the value of \(F\) is fixed exactly. The relationship between advertising and sales is not like that. Two weeks with the same advertising spend will not give the same sales, because sales depend on many other things we have not measured. Such a relationship is statistical: \(x\) determines the average value of \(y\), and individual values scatter about that average. A regression model has two parts accordingly, \[ \text {response} = \underbrace {\text {systematic part}}_{\text {depends on } x} + \underbrace {\text {random error}}_{\text {everything else}} . \]

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