What are the assumptions that need to be verified when conducting a linear regression analysis?

In a statistics course project, I conducted a linear regression analysis to explore the relationship between study hours and exam scores among students. I started by ensuring the assumptions were met. For linearity, I plotted the data and confirmed a straight-line relationship. To check independence, I ensured that each student's study hours were recorded independently. I performed residual analysis to verify homoscedasticity and found consistent variance across study hours. Finally, I checked for normality of residuals using a Q-Q plot. By verifying these assumptions, I was able to confidently conclude that increased study hours positively impacted exam scores, which my professor praised as a well-structured analysis.

During my time volunteering for a non-profit organization, I helped analyze the effectiveness of various fundraising events. I collected data on funds raised and the number of attendees. To ensure my linear regression model was valid, I checked the assumptions. I plotted the data to confirm a linear relationship between attendance and funds raised. I also ensured that the data points were independent since each event was distinct. I assessed homoscedasticity by examining the spread of residuals and found it met the criteria. This analysis helped the organization understand which events were most effective and guided their future planning, showcasing the importance of proper statistical methods even in volunteer settings.

In my first job, I was tasked with analyzing the impact of a recent marketing campaign on sales figures. I applied linear regression to model this relationship. To ensure the reliability of my results, I verified key assumptions. I plotted sales data against marketing spend, confirming the linearity assumption. I ensured that the data points were collected independently, especially since we had multiple campaigns running. Checking for homoscedasticity, I analyzed the residuals and confirmed they were evenly distributed. My analysis revealed a strong positive correlation between marketing spend and sales, which helped guide future marketing budgets. This experience taught me the importance of verifying assumptions for credible analysis.