Extrapolation vs Least-Squares Regression Line
Both terms below come up in the same part of the course, and students mix them up. Here is each one defined on its own, side by side, so you can see where they part company.
Extrapolation
Regression and correlation
Extrapolation is using a regression line to predict outside the range of x-values the data covered, where the pattern may no longer hold.
Extrapolation stretches a fitted line beyond the interval of explanatory values you actually observed, where there is no evidence the linear trend continues. Predictions there can be badly wrong because the relationship may bend, flatten, or reverse. For example, a line fit to children's ages 5 to 12 might predict a 40-year-old is 12 feet tall. Keep predictions within the observed range of the explanatory variable to stay on safe ground.
Least-squares regression line
Regression and correlation
The least-squares regression line is the straight line through a scatterplot that makes the sum of the squared residuals as small as possible.
The least-squares regression line is the best-fit line for predicting the response from the explanatory variable, chosen to minimize the total squared vertical distance from the points. Its equation is , where (read y-hat) is the predicted response, is the y-intercept, and is the slope. For example, predicts a score of 75 when hours of study. The line always passes through the point of averages .