These slides show the relationship between screen time and sleep duration

We model this relationship using a simple linear regression:

\[ y = \beta_0 + \beta_1 x + \epsilon \] where:

• \(y\): Sleep Duration (hours)

• \(x\): Screen Time (hours)

• \(\beta_0\): Intercept (expected sleep when screen time is 0)

• \(\beta_1\): Slope (change in sleep for each additional hour of screen time)

• \(\varepsilon\): Random error term

This model estimates how changes in screen time affect sleep

The average sleep duration is calculated with this formula:

\[ \bar{y} = \frac{1}{n} \sum_{i=1}^{n} y_i \] where:

• \(\bar{y}\): Average sleep duration

• \(y_i\): Sleep duration for individual \(i\)

• \(n\): Total number of individuals

library(plotly)
set.seed(42)

df = data.frame(
  ScreenTime = runif(100, 0, 12),
  Sleep = rnorm(100, mean = 8, sd = 1.5) - 0.3 * runif(100, 0, 12),
  Age = runif(100, 10, 60)
)
plot_ly(df, x = ~ScreenTime, y = ~Age, z = ~Sleep,
        type = "scatter3d", mode = "markers",
        marker = list(size = 3, color = ~Sleep, colorscale = "Viridis")) %>%
  layout(scene = list(
    xaxis = list(title = "Screen Time (hours)"),
    yaxis = list(title = "Age"),
    zaxis = list(title = "Sleep Duration (hours)")
  ))