Statistics · Ch 3 — Linear Regression

Prediction Using Regression Equations

Once the regression equation is known, prediction is simple substitution:

To estimate $Y$ for a given $X = x_0$ , substitute $x_0$ into the regression equation of $Y$ on $X$ .
To estimate $X$ for a given $Y = y_0$ , substitute $y_0$ into the regression equation of $X$ on $Y$ .

Note

Never use the wrong line for prediction — using the $X$ -on- $Y$ line to estimate $Y$ from $X$ (or vice versa) gives a mathematically different, incorrect answer, since the two lines are derived by minimizing errors in different directions. …

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