Question

Using Quantitative Reasoning
Hope researches the impact of one variable on another. She graphs the data from her research and sees that the data forms a shape that is similar to an arch. What conclusion can Hope draw from her graph?

Answer 1

An arch-shaped scatterplot indicates a non‑linear (parabolic) relationship: as the independent variable changes the dependent variable rises to a peak and then falls (or vice versa). In other words, the effect is not monotonic — there is a maximum (or minimum) value. Hope should consider fitting a quadratic model (or other curved model) to quantify the relationship and find the peak.