What are the assumptions of linear regression, and how would you check if they are met?

In my statistics class, we conducted a project analyzing factors affecting student performance. We used linear regression to model scores based on study hours and attendance. To ensure our model's validity, we first checked for linearity by plotting study hours against scores and observing a straight-line relationship. We also assessed independence by ensuring our sample was randomly selected, which minimized bias. To check for homoscedasticity, we plotted the residuals and noticed they were evenly spread, indicating constant variance. Finally, we used a normal probability plot to evaluate the normality of residuals, confirming they followed a normal distribution. This hands-on experience taught me the importance of validating assumptions in statistical models.

During my time volunteering for a local charity, I was part of a team analyzing the effectiveness of our fundraising strategies. We employed linear regression to predict the total funds raised based on variables like the number of volunteers and types of events. To ensure our findings were robust, we visually inspected scatter plots for linearity and used statistical tests to check for independence among our data points. For homoscedasticity, we generated residual plots and verified that the variance remained consistent across levels of fundraising. We also confirmed the normality of our residuals using a histogram. This experience highlighted how crucial it is to validate assumptions to derive meaningful conclusions from our data.

In my first job as a data analyst, I was tasked with analyzing sales data to identify trends. We used linear regression to understand how various factors like advertising spend and seasonal changes influenced sales revenue. I learned to check the assumptions of linear regression by examining scatter plots for linearity and conducting tests for multicollinearity among predictors. We also analyzed residuals to ensure they followed a normal distribution and verified that the residuals were randomly distributed to confirm independence. This practical application of checking assumptions not only improved our model's accuracy but also helped in making informed decisions for future marketing strategies.