In a regression model, how would you assess the goodness-of-fit, and what metrics would you use?

During my final year in college, I worked on a project that involved predicting student performance based on various factors like study hours and attendance. To assess the goodness-of-fit of our simple linear regression model, we used R-squared to see how much variance in student scores was explained by our model. We found an R-squared value of 0.75, indicating that our model explained 75% of the variability in scores. We also calculated the Mean Squared Error and found it to be quite low, which suggested our predictions were close to the actual scores. This experience taught me the importance of using multiple metrics to evaluate model performance effectively.

While volunteering for a local non-profit organization, I assisted in analyzing their fundraising data to identify trends. We built a regression model to predict future donations based on past trends. To assess the model's goodness-of-fit, we used both R-squared and RMSE. The R-squared value was 0.85, indicating a strong fit, but we also focused on RMSE to understand the average error in our predictions. This practical experience helped me realize that while a high R-squared is good, it’s equally important to look at how close our predictions were to actual values, which RMSE illuminated.

In my first job as a data analyst, I was tasked with evaluating a marketing campaign's effectiveness using regression analysis. We developed a model to predict customer engagement based on various marketing spend. To assess the model's goodness-of-fit, we primarily relied on Adjusted R-squared since we were dealing with multiple variables. The Adjusted R-squared was significantly higher than our initial model, indicating that adding more variables improved the model without overfitting. This experience reinforced the importance of understanding the context of the metrics we use and reminded me that model evaluation is an iterative process.