1. Which variable had the most variability?

To find this, I calculated the standard deviation of both Social Anxiety and GPA. So, in R, I inputted,

> sd(data$Social_Anxiety)
Standard Deviation of Social Anxiety ≈ 9.394

> sd(data$GPA)
Standard Deviation of GPA ≈ 0.389

Therefore, Social_Anxiety (9.39) had the most variability, by far, based on its much higher standard deviation compared to GPA (0.39).

2. What pattern (if any) can be observed between Social Anxiety and GPA?

The scatter plot was created using the code:
> plot(data$Social_Anxiety, data$GPA,
main = “Anxiety vs GPA”,
xlab = “Social Anxiety”,
ylab = “GPA”)

From the scatter plot created, I saw a downward trend; as Social Anxiety increases, GPA tends to decrease.

Thus, the pattern observed showed that there appeared to be a negative relationship between Social Anxiety and GPA.

This means:
* Students with higher anxiety tend to have lower GPAs.
* Students with lower anxiety tend to have higher GPAs.

3. Are there any outliers in GPA or Social Anxiety scores?

From my observation, there were no outliers in GPA scores or Social Anxiety scores. This means that all of the values fell within the expected range based on the interquartile range (IQR) method. There were no unusually high or low scores that would have been considered extreme.

4. Do GPA scores differ consistently across years?

Yes. There was a consistent upward trend in GPA scores across the academic years.

Using the codes as follows, I got the following results:

# Calculate mean GPA by Year
> tapply(data$GPA, data$Year, mean)

> # Calculate standard deviation of GPA by Year
> tapply(data$GPA, data$Year, sd)

Year Average GPA Standard Deviation
Year 1 3.07 0.35
Year 2 3.10 0.26
Year 3 3.43 0.38
Year 4 3.73 0.21

From these results, I found that:
* GPA increased each year from Year 1 to Year 4.
* The difference in means suggested that students in higher years tended to perform better academically.
* The standard deviations were relatively small, indicating that GPA scores within each year group were not widely spread out.

Therefore, to answer the question, I would say yes. GPA scores differed consistently across years, showing a positive trend as students progressed.