What are some common assumptions made when performing linear regression analysis, and why are they important?

In my statistics course, I worked on a project where we analyzed the impact of study hours on exam scores using linear regression. I learned that key assumptions, like linearity and independence of errors, were critical. For example, when I plotted the residuals, I noticed some patterns that suggested non-linearity, prompting me to rethink our model. I presented these findings in my report, emphasizing how checking assumptions helped us avoid faulty conclusions. This experience taught me that understanding assumptions is vital for making accurate predictions.

During my time volunteering for a local non-profit, I assisted in analyzing donor data to predict future contributions. I discovered that one common assumption, homoscedasticity, was violated because the variance of donations varied significantly across different income levels. By addressing this issue and using transformations to stabilize variance, we were able to improve the model's accuracy. This experience illustrated how assumptions affect real-world data analysis and the importance of addressing them to draw reliable insights.

In my first job as a data analyst, I was tasked with evaluating customer satisfaction scores based on various service metrics. I recalled my coursework and ensured that the assumptions of linear regression, such as normality and independence, were met. I conducted tests and transformations where necessary, which ultimately led to more reliable insights and actionable recommendations for improving customer service. This reinforced my understanding that verifying these assumptions is essential for delivering credible results.