• The data set that is being used is a collection of arrests in the US
• We will be using linear regression to the view relationship between the number of murder arrests and assault arrests and if a linear relationship exists betweent the two
• If so, one may be a predictor of the other

• We will use assault arrests as the variable that could possibly be used to predict murder arrests

\[Y = \beta_0 + \beta_1X+\epsilon\]

• Y: Murder arrests/100k residents
• X: Assault arrests/100k residents
• \(\beta_0\): Baseline murder arrests rate
• \(\beta_1\): Rate of murder arrests per assault arrest
• \(\epsilon\): Error

## (Intercept)     Assault 
##  0.63168266  0.04190863

## `geom_smooth()` using formula = 'y ~ x'

\[H_0: \beta_1 = 0\] \[H_a: \beta_1 \neq 0\] \[F = \frac{MSR}{MSE}\]

• Using this and the values we geet from a summary(), a F-statistic of 86.45 which produces an extremely small p-value which means that the relationship is statistically significant

plot_ly(USArrests, x = ~Assault, y = ~UrbanPop, z = ~Murder,
        type = "scatter3d", mode = "markers",
        marker = list(size = 5, color = ~Murder, colorscale = 'Viridis')) %>%
  layout(scene = list(xaxis = list(title = 'Assault'),
                      yaxis = list(title = 'Urban Pop'),
                      zaxis = list(title = 'Murder')))