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ACST8083

Actuarial Statistics

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.
1
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-
2
lection approach. (20
marks)