Final Exam

Question 5:

Consider the following vectors representing the number of field goals made and attempted by a basketball player in five games:

Field Goals Made: c(18, 7, 6, 9, 10,13) Field Goals Attempted: c(36, 23, 12, 18, 24,22)

Calculate the field goal percentage for each game and select the correct average field goal percentage for the five games.

Answer :

# Field goals made and attempted
fg_made      <- c(18, 7, 6, 9, 10, 13)
fg_attempted <- c(36, 23, 12, 18, 24, 22)

# Field goal percentage for each game, rounded to 2 decimals
fg_pct <- round((fg_made / fg_attempted) * 100, 2)

# Labeling per game
names(fg_pct) <- paste("Game", 1:length(fg_pct))

# Per-game percentages
print(fg_pct)

Game 1 Game 2 Game 3 Game 4 Game 5 Game 6 
 50.00  30.43  50.00  50.00  41.67  59.09 

# Average field goal percentage, rounded to 2 decimals
avg_fg_pct <- round(mean(fg_pct), 2)
cat("Average:", avg_fg_pct, "\n")

Average: 46.87 

Question 6:

Consider the following vectors in R representing the number of three-pointers made (3PM) and attempted (3PA) by a basketball player over a seven-game span:

Three-Pointers Made: c(3, 5, 10, 6, 3, 7, 1)

Three-Pointers Attempted: c(9, 10, 18, 12, 11, 12, 11)

Calculate both the average of the individual per-game three-point percentages and the overall (cumulative) three-point shooting percentage across all seven games. Submit your code and knitted R HTML file or RPubs link as instructed.

Answer :

# Three-pointers made and attempted over seven games
three_made      <- c(3, 5, 10, 6, 3, 7, 1)
three_attempted <- c(9, 10, 18, 12, 11, 12, 11)

# Per-game three-point percentages
per_game_pct <- (three_made / three_attempted) * 100

# 1. Average of the individual per-game percentages
avg_per_game_pct <- mean(per_game_pct)

# 2. Overall (cumulative) three-point percentage
overall_pct <- (sum(three_made) / sum(three_attempted)) * 100

# Labeling per game
names(per_game_pct) <- paste("Game", 1:length(per_game_pct))

# Results, rounded to 2 decimals
round(per_game_pct, 2)

Game 1 Game 2 Game 3 Game 4 Game 5 Game 6 Game 7 
 33.33  50.00  55.56  50.00  27.27  58.33   9.09 

print("Average of per-game:")

[1] "Average of per-game:"

round(avg_per_game_pct, 2)

[1] 40.51

print("Overall (cumulative):")

[1] "Overall (cumulative):"

round(overall_pct, 2)

[1] 42.17

Question 7:

Consider the following dataset representing the performance of baseball players in a season. It includes the following variables: PlayerID, Hits, At-Bats, Home Runs (HR), Walks (BB), and Strikeouts (SO).

PlayerID Hits At-Bats HR BB SO

1             112       400           25          50     60

2             124       450           22          60     65

3             121       380           8            19     67

4             106       500           20         150     92

5             140       402           11          55     70

Compute the On-Base Percentage (OBP) for each player and select the player with the highest OBP. Submit your code and knitted R HTML file or RPubs link as instructed.

(Formula: OBP = (Hits + Walks) / (At-Bats + Walks))

Answer :

# Player data
PlayerID <- c(1, 2, 3, 4, 5)
Hits     <- c(112, 124, 121, 106, 140)
AtBats   <- c(400, 450, 380, 500, 402)
BB       <- c(50, 60, 19, 150, 55)

# On-Base Percentage: OBP = (Hits + Walks) / (At-Bats + Walks)
OBP <- (Hits + BB) / (AtBats + BB)

# OBP for each player, rounded to 3 decimals
print("OBP by player:")

[1] "OBP by player:"

print(round(OBP, 3))

[1] 0.360 0.361 0.351 0.394 0.427

# Player with the highest OBP
best <- PlayerID[which.max(OBP)]
print("Player with highest OBP:")

[1] "Player with highest OBP:"

print(best)

[1] 5

print("Highest OBP value:")

[1] "Highest OBP value:"

print(round(max(OBP), 3))

[1] 0.427