Final Exam

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.

# Field Goals Made
field_goals_made <- c(18, 7, 6, 9, 10, 13)
# Field Goals Attempted
field_goals_attempted <- c(36, 23, 12, 18, 24, 22)
# Calculate Field Goal Percentage
field_goal_percentage <- field_goals_made / field_goals_attempted * 100
# Calculate Average Field Goal Percentage
average_field_goal_percentage <- mean(field_goal_percentage)
# Print the average field goal percentage
average_field_goal_percentage

[1] 46.86539

The average field goal percentage for the five games is 47%

Consider the following vectors representing the number of three-pointers made and attempted by a basketball player in five games:

Three-Pointers Made: c(3, 5,0, 6, 3, 7) Three-Pointers Attempted: c(9, 10, 8,12, 11, 12)

Calculate the three-point shooting percentage for each game and select the correct average three-point shooting percentage for the five games.

# Three-Pointers Made
three_pointers_made <- c(3, 5, 0, 6, 3, 7)
# Three-Pointers Attempted
three_pointers_attempted <- c(9, 10, 8, 12, 11, 12)
# Calculate Three-Point Shooting Percentage
three_point_percentage <- three_pointers_made / three_pointers_attempted * 100
# Calculate Average Three-Point Shooting Percentage
average_three_point_percentage <- mean(three_point_percentage)
# Print the average three-point shooting percentage
average_three_point_percentage

[1] 36.4899

ANS:

The average three-point shooting percentage for the five games is 36.4%

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.

1. Player 1 b) Player 2 c) Player 3 d) Player 4 e) Player 5

To calculate OBP, you can use the following formula:

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

# Create a data frame with the player data
player_data <- data.frame(
  PlayerID = 1:5,
  Hits = c(112, 124, 121, 106, 140),
  At_Bats = c(400, 450, 380, 500, 402),
  HR = c(25, 22, 8, 20, 11),
  BB = c(50, 60, 19, 150, 55),
  SO = c(60, 65, 67, 92, 70)
)
# Calculate OBP for each player
player_data$OBP <- (player_data$Hits + player_data$BB) / (player_data$At_Bats + player_data$BB)
# Find the player with the highest OBP
highest_obp_player <- player_data[which.max(player_data$OBP), ]
# Print the player with the highest OBP
highest_obp_player

NA

ANS:

The player with the highest OBP is Player 5 with an OBP of 0.43

Consider a multiple linear regression model in R: model <- lm(Goals ~ Assists + Shots + Penalties, data = dataset). Given the output we obtained, which predictor variables are statistically significant at the 0.05 significance level? Select all that apply.

Coefficients: Estimate Std. Error t-value Pr(>|t|) (Intercept) 10.2 2.1 4.85 <0.001 Assists 0.6 0.2 3.20 0.004 Shots 0.3 0.1 2.10 0.045 Penalties 0.2 0.3 0.70 0.500

Residual standard error: 2.5 on 80 degrees of freedom Multiple R-squared: 0.75, Adjusted R-squared: 0.73

# Create a data frame with the regression output
regression_output <- data.frame(
  Predictor = c("(Intercept)", "Assists", "Shots", "Penalties"),
  Estimate = c(10.2, 0.6, 0.3, 0.2),
  Std_Error = c(2.1, 0.2, 0.1, 0.3),
  t_value = c(4.85, 3.20, 2.10, 0.70),
  Pr_t = c("<0.001", "0.004", "0.045", "0.500")
)
# Check which predictor variables are statistically significant at the 0.05 significance level
significant_predictors <- regression_output[as.numeric(gsub("<", "", regression_output$Pr_t)) < 0.05, ]
# Print the significant predictors
significant_predictors

NA