What affects the accuracy of the least squares slope?

The standard deviation of b1 (its standard error) is

where

The standard error of b1 is lowest when:

  1. the response standard deviation, σ, is low
  2. the sample size, n, is large
  3. the spread of x-values is high

Implications for experimental design

To get the most accurate estimate of the slope from experimental data,

Reduce σ
σ can be reduced by ensuring that the experimental units are as similar as possible.
Increase n
Collect as much data as possible.
Increase sx
Choose to run the experiment with x-values that are widely spread.

However if the spread of x-values is increased too much, the relationship may not be sufficiently linear for a linear model to be used.

Nonlinearity is a major problem, so it is important to be able to assess whether a relationship is linear. Don't just collect data at the ends of the 'acceptable' range of x-values, even though this maximises sx.