Computing Regression Equations from Raw Data

To find the two regression equations from a set of paired observations $(X_i, Y_i)$, follow these steps:

1. Compute $n$, $\Sigma X$, $\Sigma Y$, $\Sigma XY$, $\Sigma X^{2}$, $\Sigma Y^{2}$.
2. Find the means: $\bar{X} = \dfrac{\Sigma X}{n}$, $\bar{Y} = \dfrac{\Sigma Y}{n}$.
3. Compute the two regression coefficients using the direct (raw-score) formulas:

4. Substitute $\bar{X}$, $\bar{Y}$ and the coefficients into the deviation-form equations from the previous section, and simplify into the form $Y = a + b_{yx}X$ or $X = a' + b_{xy}Y$.
5. Sanity-check: both lines must pass through $(\bar{X}, \bar{Y})$, and $b_{yx} \cdot b_{xy}$ must not exceed 1. …