Residual Variation/Examples/Arbitrary Example 1

Example of Residual Variation

Consider the set of data $\tuple {x_i, y_i}$ for $i = 1, 2, \ldots, n$.

Let a linear regression $y = a + b x$ be determined from this set of data.

Let the estimate of $y_i$ from this model be denoted $\hat y_i$.

Then the residual is given as $e_i = y_i - \hat y_i = y_i - a - b x_i$

The error mean square has the value:

$\ds \dfrac 1 {n - 2} \sum_{i \mathop = 1} n {e_i}^2$

where the divisor $n - 2$ represents the number of degrees of freedom.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): residual variation
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): residual variation