ACST8083
Actuarial Statistics
Assignment 1, Session 1 2022
Due Date: Friday 6 May 12:00pm
Total Marks Available: 60
Instructions
ˆ All students must submit an assignment of their individual own work.1
ˆ The following two components of the assignment are to be submitted via the submission
link on iLearn:
– a typed (not scanned) PDF report.
– an R file containing all the R codes used for the entire assignment.
ˆ For the PDF report, please describe and demonstrate your working steps and thought
process as clearly as possible apart from showing important numerical answers /
tables / graphs.
1Yes, your own work. Please do not submit your assignment if you violate this principle as the consequence
may be worse than not submitting at all.
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Question
In this assignment you are given a dataset of the 30 teams that played in the regular season
of the 2021-22 National Basketball Association (NBA). The data has been obtained from
Basketball Reference website and can be downloaded from iLearn as “dataset.csv”.
The following contain the descriptions of the relevant variables in the dataset:
ˆ Team: 30 teams in the NBA and the last row contains some statistics for league average.
ˆ G: total number of games played in the 2021-22 NBA regular season.
ˆ FGpct.T and FGpct.O: average field goal percentage for the team (T) and opponent (O).
ˆ FTpct.T and FTpct.O: average free-throw percentage for the team (T) and opponent
(O).
ˆ ORB.T and ORB.O: average number of offensive rebounds per game for the team (T)
and opponent (O).
ˆ DRB.T and DRB.O: average number of deffensive rebounds per game for the team (T)
and opponent (O).
ˆ AST.T and AST.O: average number of assists per game for the team (T) and opponent
(O).
ˆ STL.T and STL.O: average number of steals per game for the team (T) and opponent
(O).
ˆ BLK.T and BLK.O: average number of blocks per game for the team (T) and opponent
(O).
ˆ TOV.T and TOV.O: average number of turnovers per game for the team (T) and oppo-
nent (O).
ˆ PTS.T and PTS.O: average number of points scored per game for the team (T) and
points allowed per game to the opponent (O).
ˆ W and L: number of wins (W) and losses (L) for the season.
You have been asked to perform relevant analyses to address the following questions:
(a) Consider only the offensive side of the game, where we use the total number of points
scored per game PTS.T as the response variable. Which two variables are the most
significant predictors for the offensive performance of a team? Discuss the model findings
and interpretations from your analyses. (5 marks)
(b) Consider only the defensive side of the game, where we use the total number of points
allowed per game PTS.O as the response variable. Which two variables are the most
significant predictors for the defensive performance of a team? Discuss the model findings
and interpretations from your analyses. (5 marks)
(c) Using a linear model framework with Gaussian errors, determine the relevant variables
in predicting the number of wins for the team using the team-related statistics (i.e., the
variables associated with team (T) but not opponent (O)) listed above.
Your analysis should include data exploration, model fitting and testing, checking of
model assumptions as well as model interpretations using forward stepwise variable se-
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lection approach. (20
marks)
You are also given the following variables:
ˆ ThrPpct.T and ThrPpct.O: average 3-point field goal percentage for the team (T) and
opponent (O).
ˆ TwoPpct.T and TwoPpct.O: average 2-point goal percentage for the team (T) and op-
ponent (O).
ˆ TRB.T and TRB.O: average number of total rebounds per game for the team (T) and
opponent (O).
ˆ TS%: true shooting percentage, a measure of shooting efficiency taking into account
two-point field goals, three-point field goals and free throws.
ˆ PlayoffPrev: whether the team has qualified for playoff in the previous 2020-21 season.
You have also been tasked to answer the following questions:
(d) Consider the best simple (i.e., with a single predictor) linear regression and the final
selected model in part (c). Does adding 3-point field goal percentage onto each of these
two models significantly improve the model? Conduct relevant hypothesis testing and
discuss your findings. (5 marks)
(e) Repeat the analyses in part (c) using a suitable distribution from the exponential family
under the GLM framework. Justify why this approach may be more appropriate for the
purpose of predicting the number of wins. You are welcomed to consider the related statis-
tics for the team and also the opponent whenever appropriate and you should provide
brief justifications for the inclusion or exclusion of relevant variables in your analyses.
Note that you are not required to repeat all the relevant procedures (e.g., data explo-
ration and forward stepwise variable selection approach) conducted in part (c) and that
your model selection here should strike a balance between quantitative assessment and
qualitative considerations. Assess the model performance on predicting the number of
wins under both the selected model in part (c) and your chosen model here. (15 marks)
Please submit a written report to address the questions above, which would be read by basket-
ball fans around the globe in addition to NBA players, coaches, front office staff, broadcasters,
journalists etc. Your report should also contain recommendations to the current state of the
NBA using the insights derived from your analyses.
In addition to the quality of the analyses conducted, you will also be assessed on the clarity
of report and R codes, explanation of steps / approaches / rationales taken in solving the
questions, communication of findings / results etc. (10 marks)
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