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:
Implications for experimental design
To get the most accurate estimate of the slope from experimental data,
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.