HW1 Solutions

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Homework 1

For this homework, use knicks.csv. Try your best not to “hard code” anything. For example, there are 23 Knicks players, but try not to type the number 23 in your code. This is to keep the script as flexible as possible, incase you had to repeat this code for a completely different roster list. Use View(knicks) to look at the dataset.

• Find the average weight of the Knicks roster.
• Find the range of the weights.
• Find the standard deviation of the weights.
• Calculate the standard deviation of the weights without using either sd() or var().
• Test if there is a significant difference in the weights of point guards & shooting guards relative to the rest of the players. Hint: point guard = PG, shooting guard = SG in the Pos. column.
• Test if guards (PG, SG) tend to have lower jersey numbers than other positions, but remove the centers (C).
• Find the average experience of the players.
• Generate a vector of the names of the 5 least heavy players
• Generate a vector of the names of the 5 heaviest players
• Drop the rows where players did not go to college or they are foreign. Save this as knicks2
• Drop the College column from the dataset.
• Check if there is a significant correlation between jersey number and experience.
• Make a correlation matrix for weight, jersey number and experience.

1 - Find the average weight of the Knicks roster.

knicks <- read.csv("C:/Users/alexc/Desktop/Empirical Workshop/data/knicks.csv", stringsAsFactors = FALSE)
mean(knicks$Wt)

## [1] 218.3913

2 - Find the range of the weights.

max(knicks$Wt) - min(knicks$Wt)

## [1] 90

3 - Find the standard deviation of the weights.

sd(knicks$Wt)

## [1] 23.54056

4 - Calculate the standard deviation of the weights without using either sd() or var().

numerator <- knicks$Wt - mean(knicks$Wt)
numerator <- numerator^2
numerator <- sum(numerator)

denominator <- nrow(knicks) - 1

sqrt(numerator / denominator) #could also do (numerator/denominator)^(1/2)

## [1] 23.54056

5 - Test if there is a significant difference in the weights of point guards & shooting guards relative to the rest of the players.

t.test(knicks$Wt[knicks$Pos %in% c("PG", "SG")],
       knicks$Wt[!knicks$Pos %in% c("PG", "SG")])

## 
##  Welch Two Sample t-test
## 
## data:  knicks$Wt[knicks$Pos %in% c("PG", "SG")] and knicks$Wt[!knicks$Pos %in% c("PG", "SG")]
## t = -4.4806, df = 14.245, p-value = 0.0004972
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -49.44191 -17.46578
## sample estimates:
## mean of x mean of y 
##  203.8462  237.3000

6 - Test if guards (PG, SG) tend to have lower jersey numbers than other positions, but remove the centers (C).

t.test(knicks$No.[knicks$Pos %in% c("PG", "SG")],
       knicks$No.[!knicks$Pos %in% c("PG", "SG", "C")])

## 
##  Welch Two Sample t-test
## 
## data:  knicks$No.[knicks$Pos %in% c("PG", "SG")] and knicks$No.[!knicks$Pos %in% c("PG", "SG", "C")]
## t = -0.65027, df = 9.75, p-value = 0.5305
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -18.68041  10.26283
## sample estimates:
## mean of x mean of y 
##  13.07692  17.28571

7 - Find the average experience of the players.

mean(as.numeric(knicks$Exp), na.rm = TRUE); mean(ifelse(knicks$Exp == "R", 0, as.numeric(knicks$Exp)))

## Warning in mean(as.numeric(knicks$Exp), na.rm = TRUE): NAs introduced by
## coercion

## [1] 4.105263

## Warning in ifelse(knicks$Exp == "R", 0, as.numeric(knicks$Exp)): NAs
## introduced by coercion

## [1] 3.391304

8 - Generate a vector of the names of the 5 least heavy players

knicks$Player[order(knicks$Wt)][1:5]

## [1] "Trey Burke\\burketr01"      "Frank Ntilikina\\ntilila01"
## [3] "Dennis Smith\\smithde03"    "Kadeem Allen\\allenka01"   
## [5] "Emmanuel Mudiay\\mudiaem01"

9 - Generate a vector of the names of the 5 heaviest players

knicks$Player[order(-knicks$Wt)][1:5]

## [1] "DeAndre Jordan\\jordade01" "Enes Kanter\\kanteen01"   
## [3] "Noah Vonleh\\vonleno01"    "Henry Ellenson\\ellenhe01"
## [5] "Luke Kornet\\kornelu01"

10 - Drop the rows where players did not go to college or they are foreign. Save this as knicks2

knicks2 <- knicks[knicks$College != "" & knicks$X == "us",]
knicks2 <- knicks[!(knicks$College == "" | knicks$X != "us"),]

11 - Drop the College column from the dataset.

knicks$X <- NULL
#knicks <- knicks[,-7] #this is an example of hard coding ... what if another roster had extra columns?  Then you'd be deleting the wrong column
#knicks <- knicks[,!colnames(knicks) == "X"]
#knicks <- knicks[,-which(colnames(knicks) == "X")]
#knicks <- knicks[,is.na(match(colnames(knicks), "X"))]

12 - Check if there is a significant correlation between jersey number and experience.

cor.test(knicks$No., as.numeric(knicks$Exp))

## Warning in cor.test.default(knicks$No., as.numeric(knicks$Exp)): NAs
## introduced by coercion

## 
##  Pearson's product-moment correlation
## 
## data:  knicks$No. and as.numeric(knicks$Exp)
## t = 0.6127, df = 17, p-value = 0.5482
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.3291994  0.5635717
## sample estimates:
##       cor 
## 0.1469884

13 - Make a correlation matrix for weight, jersey number and experience.

knicks$Exp <- as.numeric(knicks$Exp)

## Warning: NAs introduced by coercion

cor(knicks[!is.na(knicks$Exp),c("Wt", "No.", "Exp")])

##             Wt        No.       Exp
## Wt  1.00000000 0.08057782 0.3759798
## No. 0.08057782 1.00000000 0.1469884
## Exp 0.37597976 0.14698842 1.0000000

knicks$Exp <- ifelse(is.na(knicks$Exp), 0, knicks$Exp)
cor(knicks[,c("Wt", "No.", "Exp")])

##             Wt        No.        Exp
## Wt  1.00000000 0.08911475 0.37758812
## No. 0.08911475 1.00000000 0.09131957
## Exp 0.37758812 0.09131957 1.00000000