What are the potential consequences of violating the assumptions of a linear regression model?

During my final year in college, I worked on a project analyzing the relationship between study hours and exam scores among students. We initially assumed a linear relationship, but after conducting residual analysis, we found that increased study hours had diminishing returns on exam scores. This indicated that our linear regression model violated the linearity assumption. As a result, we adjusted our approach by applying a polynomial regression model, which better captured the nuances in the data. The revised model provided more accurate predictions and insights, teaching me the importance of validating model assumptions before drawing conclusions.

In a volunteer role for a local charity, I helped analyze fundraising data to understand the impact of various events on donations. We used linear regression to model the relationship between the number of events and total donations. However, we overlooked checking for independence among events, which led to overestimating the impact of one event on total donations due to clustering. This experience highlighted the necessity of validating assumptions like independence to avoid misleading results. We learned to include checks for multicollinearity and to use alternative models, which ultimately helped us make better decisions for future fundraising strategies.

In my first job as a data analyst, I was tasked with forecasting sales using a linear regression model. I noticed that the residuals were not randomly distributed, suggesting a violation of the homoscedasticity assumption. This led to unreliable confidence intervals and incorrect predictions for future sales. To address this, I implemented a weighted least squares approach, which improved the model's accuracy. This experience reinforced the importance of regularly checking model assumptions and how addressing them can significantly enhance the quality of insights drawn from data.