What are the assumptions of linear regression, and why are they important for the validity of the results?

In college, I worked on a project where we analyzed student performance based on study hours and exam scores using linear regression. We ensured the assumptions were met by plotting the data and checking for linearity. When we assessed independence, we made sure that each student's scores were recorded separately without any influence from peers. It was essential to confirm normality in our residuals, which we did by creating Q-Q plots. By validating these assumptions, we could confidently present that increased study hours positively correlated with better exam scores, which was well-received by our professors.

During my time volunteering with a local community organization, I helped analyze survey data regarding community engagement. We used linear regression to understand the relationship between community event attendance and participant satisfaction. To adhere to the assumptions, we double-checked for homoscedasticity by plotting residuals against predicted values. We also ensured that the events were independent by analyzing responses from different community members. This analysis helped the organization tailor future events based on community feedback, demonstrating how proper assumption validation can lead to actionable insights.

In my first job as a marketing assistant, I helped evaluate the effectiveness of a new campaign using linear regression. We had to check for multicollinearity among our independent variables, such as social media engagement and email open rates, to ensure our model's accuracy. By confirming that our data met the necessary assumptions, we presented our findings to the management, showing that the campaign significantly increased customer engagement. This experience taught me the value of assumption validation in making data-driven decisions.