Learning outcomes
- explain what a fitted line is
- understand why a best-fit line is useful
- connect fitted lines to prediction carefully
- avoid overclaiming from the line
What is fitting a line?
- Fitting a line means finding a line that represents the general trend in scatterplot data.
- The line summarizes linear association between two numerical variables.
Why fit a line?
- to see the overall trend clearly
- to summarize the relationship
- to make approximate predictions within the observed range
Interpretation
- upward fitted line -> positive association
- downward fitted line -> negative association
- flatter line -> weaker trend in direction
Prediction caution
- A fitted line gives approximate prediction, not certainty.
- Predictions far outside observed data are risky.
Exam hints and traps
- The fitted line does not pass through every point.
- A best-fit line is useful mainly when the scatterplot is roughly linear.
- Do not use it blindly when the pattern is clearly curved.
- Prediction beyond observed range is extrapolation and may be unreliable.
Quick practice
- Does a fitted line need to pass through all points?
- When is fitting a line most appropriate?
- Why is extrapolation risky?
Answer key
- No
- When the scatterplot shows a roughly linear pattern
- Because the trend may not continue outside the observed data range