Assignment 5
STAT 321 Winter 2025
Due: Friday April 4, 5:00PM
Accepted: Monday April 7, 11:59PM
In this final assignment, you will perform a complete linear regression analysis of an example dataset. You may choose from one of three preloaded datasets. You can use the following commands to load data and view the documentation of each dataset, replacing [name] by one of chredlin, seatpos, or teengamb.
data <- faraway::[name]
?faraway::[name]
For your chosen dataset, select one of the continuous variates as a response and use the remaining variates as potential predictors in a multiple linear regression model. Your goal is to produce a good predictive model for your chosen response.
1. (2 points) In 2-3 complete sentences, briefly describe your chosen dataset and why you have selected a particular response variate.
2. (2 points) Produce at least 2 exploratory plots or contingency tables and comment on at least one pattern you see in each plot or contingency table.
3. (4 points) Perform criterion-based model selection to choose a subset of predictors for your model. Consider at least 3 transformations or interactions of predictors that are not present in the original dataset.
4. (2 points) Produce at least 2 diagnostic plots to assess the assumptions of the multiple linear regression model. Comment on at least one pattern you see in each plot.
5. (2 points) Perform a Box-Cox analysis on your selected model. Comment on why a transformation of the response is or is not appropriate. If you feel that a transformation is appropriate, re-fit your model with the new transformed response.
6. (2 points or n/a) If you re-fit a new model in Step (5), reproduce the 2 diagnostic plots from Step (4). Comment on any changes you see in the new diagnostic plots.
7. (2 points) Report R2 and s2 for your final model and interpret them in the context of the problem.
8. (2 points) Report coefficient estimates, and 95% confidence intervals for each coefficient in your final model.
9. (3 points) Perform. 3 hypothesis tests. Report the p-values and rejection decisions, and interpret them in the context of the problem.
(a) H0 : βk = 0 vs H1 : βk ≠ 0 for one of the coefficients in your final model.
(b) H0 : βk - βℓ = 0 vs H1 : βk - βℓ ≠ 0 for one contrast of coefficients in your final model.
(c) ANOVA for simultaneous inference on 2 or more coefficients in your final model.
10. (2 points) Remove the highest influence case from your data and see if the three hypothesis tests in Step (9) have the same outcome. Note: this is a common way to assess whether a potential outlier observation is affecting our statistical conclusions.
11. (3 points) Report 95% prediction intervals under your model for at least 3 different new, artificial cases.
12. (4 points) In 2-3 complete sentences, make at least 2 conclusions about your dataset which are supported by your final model.
Additional instructions:
– The official due date for this assignment is Friday April 4 at 5:00PM on Crowdmark. Assignments will be accepted without penalty until Monday April 7 at 11:59PM on Crowdmark, after which point the usual late submission rules will apply. Note that AAS or absence-related extensions will be applied to the official due date.
– If you are unsure how to use an R function, its documentation can be viewed by typing a question mark and then the function name (i.e. ?function) into the RStudio console.
– Unless otherwise specified, you may use results from lecture without additional justi- fication. Results from the reference textbooks can be used, but you should show all steps for full marks.
– This assignment will be graded out of 30 (or 28) points. Per the course outline, in normal circumstances it will count for 5% of your final grade.
– Assignment solutions, including code, should be submitted on Crowdmark. If the as- signment is submitted with written solutions but no supporting code, it will be graded as normal, but the point total will be multiplied by 0.75.
– If you experience technical difficulties using Crowdmark,
1. Consult Crowdmark Help
2. Watch this short video about submitting an assignment on Crowdmark
3. As a last resort, if you cannot upload your assignment to Crowdmark before the deadline, email it to [email protected], so I have proof that you com- pleted your assignment on time.
– If you choose to submit typed solutions, please also email me the . tex or RMarkdown files used to compile your solutions.
– Rules regarding extensions for (formally documented) absences and grades for late submissions are provided in the course outline on Learn.