text: Errors in Extrapolations (Investigation) | NCEA Level 2 Maths | NZ Level 7 (NZC) Level 2 (NCEA) | Mathspace
  Interpreting Information from Fitted Lines I
  Interpreting Information from Fitted Lines II
  Errors in Extrapolations (Investigation)
  Interpretion of Data with Awareness of Issues (Investigation)
  Associations in Biometric Data (Investigation)
  Consider a statistical experiment in which it is assumed that the values taken by a variable that is being studied depend on values taken by an independent variable. Suppose a number of trials of the experiment have been carried out. We would feel justified in making predictions about what will occur in further trials provided the independent variable takes values that are within the range of values already tested. Such predictions are called interpolations.
  Displayed graphically, with a linear trend-line inserted, we have:
  According to the linear regression, the height $h$h as a function of the day number $d$d is approximately $h=5.6d-1.6$h=5.6d−1.6.
  In the wild, a female rabbit lives for about a year on average and in that time can have around $20$20 offspring. Suppose roughly $5$5 of these are females who themselves survive to maturity and begin to reproduce. Imagine that to a small island previously uninhabited by rabbits, a breeding pair is introduced. Ecologists then observe the above breeding pattern over a period of four years.
  If you were to use this formula to predict the number of female rabbits that were living on the island after $30$30 months, you could be confident of your answer. However, if you wished to make a prediction about the number of female rabbits that would be living on the island after 10 years, the formula would give an impossible answer of close to one hundred million female rabbits.