Explain an interaction effect to a non-statistician

WHAT THIS TESTS: Whether you can translate a statistical interaction into an intuitive picture and a business action, and whether you recognize that a single averaged coefficient would dangerously hide a sign reversal across segments.

A GOOD ANSWER COVERS: First, frame the concept without the word interaction: explain that the payoff from ad spend is not one fixed number, it depends on who you are spending on. For young users every extra dollar drives more sales, while for older users it does little or even slightly backfires. The clearest visualization is an interaction plot, also called a marginal-effects or predicted-values plot: put ad spend on the x-axis and predicted sales on the y-axis, and draw a separate line for each age segment. The under-30 line slopes up steeply while the over-50 line is flat or tilts down, so the difference in slopes is immediately visible without any statistics. Avoid coefficient tables. Then convert it into a decision: because the return on ad spend is concentrated in younger users, reallocate budget toward them and pull back on the segment where it does not pay off, with a caveat to confirm causality before acting at scale.

COMMON WRONG ANSWERS: Reporting a single average effect of ad spend, which nets the positive and negative slopes into a misleading middle number. Showing raw regression coefficients and interaction terms to a non-technical audience.

LIKELY FOLLOW-UPS: How confident are you this is causal and not confounded? Should you split into more age bands? How would you A/B test the reallocation?

ONE CONCRETE EXAMPLE: The analyst shows two lines on one chart: spend versus predicted sales for under-30s rising sharply and for over-50s sloping gently down. The director instantly sees that ad dollars work on the young and not the old, and agrees to test shifting budget toward the younger segment.