Validating Regression Analysis Assumptions in Practice

An education research analyst needed to untangle collinear behavioral variables to understand their independent impacts on student exam performance. Using a scatter plot, they visualized the relationship between study hours per day (scaled 0 to 8) and exam scores (scaled 20 to 100). A solid blue linear fit line showed a strong positive correlation, rising from a score of roughly 50 at zero hours to near 100 at seven hours. To address collinearity, a mental health rating was mapped to a color scale (orange at 2 to green at 10). Green points clustered above the trendline, while orange and purple fell below. This visual inspection prepared the analyst for controlled multiple regression models.

What it shows:

Visualizing overlapping variables helps analysts inspect collinearity before running controlled regression models.

An international trade economist used a dashboard to diagnose gravity model regressions analyzing trade openness across 30 major economies. Initially, a scatter plot showed a baseline relationship between Log GDP and Trade Openness with an OLS slope of -24.49, suggesting larger economies are less open. However, a coefficient detail table revealed how expanding the model to include population solved a proxy-variable bias. The Log GDP estimate collapsed to a statistically insignificant -0.92, while Log Population captured the negative effect at -20.69. A supplementary table ranked outliers like Singapore (340.35%) and Ireland (222.98%). Surfacing these shifts prevented flawed macroeconomic conclusions.

What it shows:

Expanding baseline models with additional variables can expose and correct critical proxy-variable bias.