Question

Justifying Predictions of a Scatterplot
Can predictions be made of a scatterplot that shows no association? Explain your answer.

Answer 1

Short answer: Not really — at least not useful ones.

Explanation:
- A scatterplot that shows no association means the explanatory (x) and response (y) variables are unrelated in the data. A fitted line will have slope ≈ 0, correlation r ≈ 0 and R² ≈ 0. That implies x explains none (or almost none) of the variation in y.
- Because of that, knowing x does not improve your estimate of y. The best constant prediction you can make is the overall mean (or median) of y, but those predictions ignore x and will have large errors and wide prediction intervals.
- You also cannot reliably extrapolate beyond the observed x values, and any “pattern” you see is likely just random scatter.

Caveat: A scatterplot that appears to show no association might hide a relationship (nonlinear, conditional on another variable, or masked by noise) or be limited by small sample size. In that case you should try transformations, look for other predictors, or collect more data.