What affects standard errors?

This page demonstrates the main influences on the accuracy of estimating β1.

The standard error is lowest when:

  • the response standard deviation, σ, is low
  • the sample size, n, is large
  • the spread of x-values is high

Demonstrate each by adjusting σ, n and sx then building up the sampling distributions in a simulation.

Mention that for accuracy, experimental data should be collected with:

  • low σ (i.e. minimum variability in the experimental units)
  • large n (i.e. collect as much data as possible)
  • a big spread of x-values (if they can be controlled)

Mention that a big spread of x-values does however lead to the potential problem of nonlinearity.