This Assignment focuses on the model-building process using multiple regression.
The overall goal of this assignment is to demonstrate your understanding of the key topics in this unit and that you can apply them in a real-world situation.
Your goal is to determine which demographic factors are most closely associated with cancer deaths (Death Rate) in these areas. In identifying these you hope to create a sound argument that improvement in some or all the underlying factors (independent variables), could lead to a reduction in cancer mortality rates (the dependent variable).
You have been tasked with doing the initial research, developing a good model, and writing up your findings in a report to the governing board.
Build a multiple linear regression model with the test data (Note your test data is your sample data (n=50), using the steps in model building as discussed in class – write a summary of your analysis (maximum of 3 pages) and do a 5-minute video presentation of your results.
Interpret the results of your initial EDA on the test data. Use visuals, a correlation matrix, and regression statistics to support a discussion of your first impressions on the strength of the initial model and on which x variables appear to look like promising candidates and why.
Discuss the process by which you reduced the model by eliminating unhelpful x variables. Briefly discuss each iteration of the model, which x variables were eliminated and why.
Using the best subsets regression approach, describe which models were left. Then use the root mean squared error (RMSE) and the adjusted R-squared statistics to compare the performance of your models. You may create a table here that summarises both.
Perform a hypothesis t-test for the regression slope on all the remaining x variables and do an F-test on the whole model. Be sure to include all steps, including a discussion of Type I and II errors. Use ∝=0.01. Construct a 99% confidence interval estimate of the population slopes.
Interpret all the features of the best model, i.e. the slope coefficients and p values, including each of the confidence intervals for the slopes of all remaining x variables. Finally, predict the cancer death rate using your test data – this will tell you something important about the predictive quality of your best model.
