2025-09-13

Slide 1: The Freshman 15

Statistical Decline in Physical Activity During Freshman Year

The Freshman 15 need for minutes of exercise!

Slide 2: Background

Slide 3: Simulated Data and Real Research Benchmarks

  • Based on Vadeboncoeur et al. (2015): average weight gain ≈ 1.36 kg over ~5 months; ~61% gain weight

  • Based on [PMC2532948] article: decline in exercise and physical activity observed in freshman year.

  • To study the decline statistically, we simulate data for 30 students at 3 time points: Month 1, Month 3, and Month 6.

  • Assume their weekly activity (minutes) starts higher and declines linearly over time.

  • I’ll use this simulated data to build a regression model, make plots, and test: is the decline statistically significant?

Slide 4: Simulated Data Set + code

set.seed(2025)
students <- rep(1:30, each = 3)
month <- rep(c(1, 3, 6), times = 30)

##simulation with activity approx. 200 minutes/week and declining 
##15 minutes/month plus normal noise
activity <- round(rnorm(90, mean = 200 - 15 * month, sd = 20))
df <- data.frame(Student = factor(students),
                 Month = month,
                 Activity = activity)
head(df)
##   Student Month Activity
## 1       1     1      197
## 2       1     3      156
## 3       1     6      125
## 4       2     1      210
## 5       2     3      162
## 6       2     6      107

Slide 5: Animated Average Activity by Month

Slide 6: Activity Distribution by Month in ggplot2

Slide 7: Interactive Scatterplot using plotly in 3D

Slide 8: Linear Regression Equation

Let’s fit a linear regression to predict weekly activity as a function of month:

\[ \hat{Activity} = \beta_0 + \beta_1 \cdot \text{Month} \]

Where:

  • \(\hat{Activity}\) = predicted weekly minutes of activity

  • \(\beta_0\) = intercept (activity level at month 0)

  • \(\beta_1\) = slope (the change in activity per month)

From simulated model:

\[ \hat{Activity} = 200 - 15 \cdot \text{Month} \]

Slide 9: The interpretation of Linear Regression Equation

  • Students start with ~200 minutes per week of activity

  • On average, students lose ~15 minutes of activity per month

  • This downward trend is consistent with published research of physical activity for college students

Slide 10: Hypothesis Test for Regression Slope

Test whether the activity declines significantly over time, perform hypothesis test on the slope \(\beta_1\) in the model:

\[ \hat{Activity} = \beta_0 + \beta_1 + \cdot + \text{Month} \]

Slide 11: Hypotheses–

\[ H_0: \beta_1 = 0 \quad \text{(no change in activity over time)} \\ H_a: \beta_1 < 0 \quad \text{(activity declines over time)} \]

If the p-value is small (typically less than 0.05), we reject \(H_0\) and conclude that physical activity does decline significantly as months increase.

Slide 12: Summary and Conclusion

  • Simulated data showing weekly physical activity for 30 college students in months 1, 3, and 6
  • The data showed a clear declining trend, consistent with published research
  • A linear regression model estimated a 15-minute-per-month decline in weekly activity
  • This aligns with studies showing reduced physical activity and weight gain during freshman year.
  • The analysis supports the conclusion that students’ physical activity significantly declines over their first college semester
  • Future studies could include more time points, multiple semesters, or interventions to test the effectiveness of wellness programs.

Slide 13: References

  • Vadeboncoeur, C., Townsend, N., & Foster, C. (2015). A meta-analysis of weight gain in first year university students: Is freshman 15 a myth? BMC Obesity, 2, 22. https://doi.org/10.1186/s40608-015-0051-7

  • Bray, S. R., & Born, H. A. (2004). Transition to university and vigorous physical activity: Implications for health and psychological well-being. Journal of American College Health, 52(4), 181–188. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2532948/

  • Simulated data created by author based on trend estimates in cited studies.