Regression Parameters and Technology

Enter paired observations into two lists and calculate Pearson’s r and the required linear regression using technology. Inspect the scatter first: r measures linear association, not every possible relationship. Its sign gives direction and |r| gives strength. A line of best fit drawn by eye should pass through (x, y). The fitted regression lines also pass through this mean point. **Given information** | **Use** x, predict y | Regression of y on x: y=ax+b. y, predict x | Regression of x on y: x=cy+d. Example: a fitted line y=2.4x+7 predicts y=31 at x=10. The slope predicts an increase of 2.4 response units for one extra input unit. The intercept predicts 7 response units at x=0; it may lack practical meaning if zero is outside the observed range. Rearranging this line does not generally give the reverse regression. Check prediction reliability in context: interpolation stays inside the observed input range, while extrapolation extends beyond it. Even interpolation may be unreliable if the scatter is curved or widely spread, an influential outlier affects the fit, or the population or conditions have changed. A large absolute correlation does not justify extrapolation. For inputs observed from 10 to 40, prediction at 25 is interpolation and at 60 is extrapolation.