Overview

A student survey was conducted at a major university. Data were collected from a random sample of 239 undergraduate students, and the information that was collected included physical characteristics (such as height, handedness, etc.), study habits, academic performance and attitudes, and social behaviors. In this report, I will focus on exploring relationships between some of those variables.

Raw Data

The data observes individual undergrads, and contains the following variables:

load("body_image.RData")
x<-data
head(x)
##   Gender Height  GPA HS_GPA Seat  WtFeel Cheat
## 1 Female     64 2.60   2.63    M AboutRt    No
## 2   Male     69 2.70   3.72    M AboutRt    No
## 3 Female     66 3.00   3.44    F AboutRt    No
## 4 Female     63 3.11   2.73    F AboutRt    No
## 5   Male     72 3.40   2.35    B  OverWt    No
## 6 Female     67 3.43   3.84    M AboutRt    No

Q1. Is there a relationship between students’ college GPAs and their high school GPAs?

q1 <- x[,c(3,4)]
q1 <- na.omit(q1)

r <- cor(q1$HS_GPA, q1$GPA, use="c")
plot(q1$HS_GPA, q1$GPA, main="High School vs College GPA", xlab="HS GPA", ylab="College GPA", pch=19, cex=.5)

l = lm(q1$GPA~q1$HS_GPA)
abline(l, col="red")
cf=coefficients(l);

text(2, 4.1, paste("GPA = ",round(cf[1],2),"+",round(cf[2],2),"HS_GPA"), col="red")
text(1.8, 3.85, paste("r = ", round(r,3)))
rect(1.45, 4.35, 2.6, 3.65)

We see that there exists a moderately strong, positive linear relationship between high school GPA and college GPA. Although college GPAs are generally a bit lower (as is likely the result of increased difficulty and less, if any >4.0 weighting), high school GPA proves to be a decent predictor of college performance.

Q2. Are there differences between males and females with respect to body image?

# remove NA values 
q2 <- x[,c(1,6)]
q2 <-na.omit(q2)

Gender vs Body Image

tbl = table(data.frame(q2$Gender, q2$WtFeel), dnn=c("Gender", "Body Image"))
colnames(tbl)<-c("About Right", "Overweight", "Underweight")
tbl
##         Body Image
## Gender   About Right Overweight Underweight
##   Female         107         32           6
##   Male            56         15          13

Body Image by Gender

colnames(tbl)<-c("% About Right", "% Overweight", "% Underweight")
round(100*tbl/rowSums(tbl))
##         Body Image
## Gender   % About Right % Overweight % Underweight
##   Female            74           22             4
##   Male              67           18            15

Around 66% of men and 74% of women feel that their weight is about right. When looking at the proportions of each, who feel some sort of dissatisfaction, we see that a higher percentage of women feel overweight (22% vs 18%), and far more men feel underweight than women (15% vs 4%).