DSCI 304 PSET 1
Matt Lawrence
2026-09-10
#Practice Set 1
#q1
Batting <- read.csv("MLB Batting Data.csv")
library(dplyr)## Warning: package 'dplyr' was built under R version 4.4.3##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionsum(Batting$batting_avg>=0.300)## [1] 106#answer was 106
#q2
Batting$HitByPitch_NewVar <- NA
Batting$HitByPitch_NewVar[Batting$b_hit_by_pitch>=1] <-1
Batting$HitByPitch_NewVar[Batting$b_hit_by_pitch==0] <- 0
table(Batting$HitByPitch_NewVar)##
## 0 1
## 29 700#29 weren't hit at least once, 700 were at least once.
#q3
X <- Batting$exit_velocity_avg
Y <- Batting$b_home_run
reg <- lm(Y~X)
summary(reg)##
## Call:
## lm(formula = Y ~ X)
##
## Residuals:
## Min 1Q Median 3Q Max
## -22.5319 -5.5319 -0.2615 5.3555 28.1160
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -217.6313 11.1088 -19.59 <2e-16 ***
## X 2.7042 0.1254 21.57 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.941 on 727 degrees of freedom
## Multiple R-squared: 0.3901, Adjusted R-squared: 0.3893
## F-statistic: 465.1 on 1 and 727 DF, p-value: < 2.2e-16plot(X, Y, xlab="Exit Velocity Average", ylab="Home Run Number", main="Question 3 Regression")
plot(reg$residuals)
#There is a general association of an increase in Exit Velocity Average is associated with Home Run Number increase,
#but adjusted r^2 is 0.3893 which implies r is about 0.6239, which is a moderate association. Also after looking at the returned
#regression coefficient associated (beta_1) which was 2.7042, this is a positive number also suggestion the positive association
#between the two variables. This value is also statistically significant since it has a P-Value less than 0.05. I would say the
#conventional wisdom is somewhat correct.
#q4
x <- Batting$player_age
y <- Batting$batting_avg
reg2 <- lm(y~x)
summary(reg2)##
## Call:
## lm(formula = y ~ x)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.100959 -0.018464 -0.000835 0.019041 0.077603
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.2829787 0.0077558 36.49 <2e-16 ***
## x -0.0004381 0.0002656 -1.65 0.0995 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.02707 on 727 degrees of freedom
## Multiple R-squared: 0.003729, Adjusted R-squared: 0.002359
## F-statistic: 2.721 on 1 and 727 DF, p-value: 0.09946#not stat sig beta 1, low r
Batting$age_new <- NA
Batting$age_new[Batting$player_age<30] <- 0
Batting$age_new[Batting$player_age>=30] <- 1
x2 <- Batting$age_new
reg3 <- lm(y~x2)
summary(reg3)##
## Call:
## lm(formula = y ~ x2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.099747 -0.018747 -0.000042 0.018958 0.079253
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.272042 0.001301 209.134 <2e-16 ***
## x2 -0.004294 0.002038 -2.107 0.0355 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.02704 on 727 degrees of freedom
## Multiple R-squared: 0.00607, Adjusted R-squared: 0.004703
## F-statistic: 4.44 on 1 and 727 DF, p-value: 0.03545#better beta 1
#q5
Slugging <- function(Batting){
slugging_percentage <- data.frame(((Batting$b_single) + (2*Batting$b_double)
+ (3*Batting$b_triple) + (4*Batting$b_home_run))/(Batting$b_ab))
return(slugging_percentage)
}
Slugging(Batting)## X..Batting.b_single.....2...Batting.b_double.....3...Batting.b_triple....
## 1 0.3832976
## 2 0.3861720
## 3 0.4171429
## 4 0.3987207
## 5 0.4160839
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## 728 0.4672897
## 729 0.3996540slug <- Slugging(Batting)
percentage <- slug$X..Batting.b_single.....2...Batting.b_double.....3...Batting.b_triple....
mean(percentage)## [1] 0.4568072#0.04568072
sum(percentage > 0.500)## [1] 183#183
#q6
#A
Batting_Subset <- subset(Batting, Batting$year=="2019")
sum(Batting_Subset$year==2019)## [1] 156#156
#B
mean(Batting_Subset$b_total_pa)## [1] 588.4359#588.4359
#C
max(Batting_Subset$b_home_run)## [1] 53#53
Batting_Subset$first_name[Batting_Subset$b_home_run==53]## [1] " Pete"#pete
Batting_Subset$last_name[Batting_Subset$b_home_run==53]## [1] "Alonso"#alonso