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Consider the [[mathematical model|model]] function
: <math> y = \alpha + \beta x,</math>
which describes a line with slope {{mvar|β}} and {{mvar|y}}-intercept {{mvar|α}}. In general, such a relationship may not hold exactly for the largely unobserved population of values of the independent and dependent variables; we call the unobserved deviations from the above equation the [[errors and residuals|errors]]. Suppose we observe {{mvar|n}} data pairs and call them {{math|{(''x''<sub>''i''</sub>, ''y''<sub>''i''</sub>), ''i'' {{=}} 1, ..., ''n''}}}. We can describe the underlying relationship between {{math|''y''<sub>''i''</sub>}} and {{math|''x''<sub>''i''</sub>}} involving this error term {{math|''ε''<sub>''i''</sub>}} by
: <math> y_i = \alpha + \beta x_i + \varepsilon_i.</math>
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