A researcher at a university wants to better understand how study habits affect student grades. To determine whether there is a link between hours spent studying and exam scores, the researcher recruits fifty students in an advanced calculus class to record their study hours over the semester, and also obtains permission to see their scores on the final exam. Perform a regression analysis, where the average number of hours spent studying per week over the two-month data collection period is the independent variable and the score on the final exam is the dependent variable. Be sure to include the residuals and residual plot in your analysis.