What are the assumptions of linear regression, and how do violations of these assumptions affect the results?

During my final year in college, I worked on a project analyzing the impact of study hours on academic performance. To model this relationship, we used linear regression. I learned that the key assumptions included linearity, which means the relationship should be a straight line; independence, where errors shouldn't be correlated; and homoscedasticity, meaning residuals should have constant variance. We initially ignored checking these assumptions and found that our model predictions were inaccurate. After revisiting our data and applying transformations, we confirmed the assumptions were met, leading to more reliable conclusions. This experience taught me the importance of validating assumptions in statistical modeling.

As part of a volunteer project for a local NGO, I helped analyze survey data on community health awareness. We used linear regression to assess how various factors influenced awareness levels. I realized that we needed to ensure our data met the assumptions of linear regression. For instance, we checked for homoscedasticity by plotting residuals and found some patterns indicating a violation. To address this, we used weighted least squares regression, which improved our model's accuracy. This experience highlighted how crucial it is to understand and check assumptions, even in volunteer projects, to draw valid conclusions from data.

In my internship at a market research firm, I was tasked with analyzing consumer behavior data using linear regression. With about a year of experience, I understood the assumptions behind the model. However, I encountered a situation where our data showed signs of multicollinearity, violating the independence assumption. This led to inflated standard errors and made it difficult to interpret our results. By discussing the issue with my supervisor, we decided to remove some correlated predictors and re-ran the regression. The revised model provided clearer insights, underscoring the importance of adhering to assumptions in statistical analysis and the real impact of violations.