Question: Two variables y and x are believed to be related by the following stochastic equation:
y = α + βx + µ
where u is the usual random disturbance with zero mean and constant variance σ2. To check this relationship one researcher takes a sample size of 8 and estimates β with OLS. A second researcher takes a different sample size of 8 and also estimates β with OLS. The data they used and the results they obtained are as follows:
Can you explain why the standard error of β^ for the first researcher is larger than the standard error of β^ for the second researcher?