There are generally two different methods for calculating Rate of Improvement from an academic sense.

• The simple model. y=(x2 - x1) / w
  • Where y = ROI, x₂  = last data point, x₁ = first data point, w = number of weeks between x₂ and x₁
  • The problem with this method is it ignores fluctuations within the period between x₂ and x₁
  • In the example below, the ROI calculated using this method would be 1.52. However this does not represent the actual growth of the student - as they didn't see a surge in test scores until the last three data points.

• The Linear Regression model. y = mx + b
  • y = mx + b is not the formula of a linear regression - but we use the linear regression to get the components of the slope of a line formula - which gives us our ROI.
  • Where y = ROI, m = slope, x = Date, b = intercept
  • Using a linear regression for calculating ROI is much more reliable as it takes into account the fluctuations in scores - and levels outliers.
  • In the example above, the intervention ROI is 1.36 - which is much more telling of the progress the student made.