STSCI 4030-5030 Lab 1

# Set up environment
rm(list = ls())
library(ggplot2)
library(tibble)

Task 1

Using the random number seed 1234, generate 1000 draws from a normal distribution with mean 100 and standard deviation 20. Plot a histogram of these draws and add the following details:

• Set number of breaks to 20.
• Change from plotting the frequency to the probability.
• Add title that states the sample mean: “Sample mean = x, Sample variance = y”. Do not hard code these values.
• Add a red line using lines() to plot the probability density function of the normal distribution we generated the data from.

Use ?hist for more information about plotting options for the histogram.

set.seed(1234)
DATA <- rnorm(100, mean = 100, sd = 20)
hist(DATA,
     breaks = 20, #number of bins
     freq = F, #Display probability density instead of frequency
     main = paste("Sample mean = " , round(mean(DATA), 2) , ", Sample Variance = " , round(var(DATA), 2)),
     )
seq <- seq(min(DATA), max(DATA), length = length(DATA)) #Arrange the data in order
lines(seq, dnorm(seq, mean = mean(DATA), sd = sd(DATA)),  col = "red", lwd = 2)

Task 2

a)

Download nba_wingspan.csv from Canvas. It contains data on the height and wingspan (in inches) of NBA players, taken from here.

Import this data, generate a scatterplot of wingspan versus height, and add the OLS line of best fit to it. Add a title and label the axes.

Report the estimates from the model for \(\beta_0\) and \(\beta_1\).

#Import data
setwd("~/Desktop/R/STSCI 5030")
NBA = read.csv("Data/nba_wingspan.csv", header=TRUE)
plot(NBA$wingspan, NBA$height, main = "Scatterplot of wingspan vs height", xlab = "wingspan", ylab = "height")
OLS <- lm(NBA$height ~ NBA$wingspan)
abline(OLS, col = "blue", lwd =2)

\(\beta_0\) =

OLS$coefficients[1]

## (Intercept) 
##    20.54038

\(\beta_1\) =

OLS$coefficients[2]

## NBA$wingspan 
##    0.6989063

b)

Now create a subset of the dataset containing only players who play Center position, pos equal to C, and generate the plot again like in part a). Add a title and label the axes.

Report the estimates from the model for \(\beta_0\) and \(\beta_1\).

Center <- NBA[NBA$pos == "C", ]
plot(Center$wingspan, Center$height, main = "Scatterplot of wingspan vs height in Cetner", xlab = "wingspan", ylab = "height")
OLS_c <- lm(Center$height ~ Center$wingspan)
abline(OLS_c, col = "blue", lwd =2)

\(\beta_0\) =

OLS_c$coefficients[1]

## (Intercept) 
##     68.9505

\(\beta_1\) =

OLS_c$coefficients[2]

## Center$wingspan 
##       0.1534844

Task 3

Submit both your .Rmd file and the resulting .html file in Canvas.