What are the assumptions underlying linear regression, and how can violations of these assumptions affect your results?

In my statistics course, I worked on a project analyzing the impact of study habits on exam scores. We used linear regression to predict scores based on hours studied, attendance, and previous grades. While preparing, I learned about the assumptions of linear regression, such as linearity and normality. During our analysis, we found that our data didn’t meet the normality assumption, which could lead to unreliable results. To address this, we applied transformations to our data, which helped us achieve better accuracy in our predictions. This experience made me appreciate the importance of verifying assumptions before drawing conclusions.

While volunteering for a local charity, I helped analyze the impact of different fundraising strategies on the amount raised. We collected data on various events and used linear regression to assess which methods were most effective. I discovered the significance of the independence assumption when we noticed that some events overlapped, potentially skewing our results. We decided to isolate the data for each event, ensuring that each observation was independent. This taught me how important it is to consider assumptions in practical situations and how they can affect the outcomes of our analyses.

In my first job as a data analyst, I worked on analyzing sales performance using linear regression. I quickly realized that multicollinearity was an issue in our dataset, as some predictors were highly correlated, which affected the stability of our coefficient estimates. To mitigate this, we used variance inflation factors to identify these variables and adjusted our model accordingly. This experience underscored the importance of assumption checks and how they can significantly influence the accuracy and reliability of our predictive models in a business context.