A possible drawback to this method is that by reducing the number of data points, the degrees of freedom associated with the residual error is reduced, thus potentially reducing the power of the test. If the data are in a particular order, consider the possibility of dependence. For serially correlated Y values, the estimates of the slope and intercept will be unbiased , but the estimates of their variances will not be reliable. If you are unsure whether your Y values are independent, you may wish to consult a statistician or someone who is knowledgeable about the data collection scheme you are using. Values may not be identically distributed because of the presence of outliers .
Outliers are anomalous values in the data.
Outliers may have a strong influence over the fitted slope and intercept, giving a poor fit to the bulk of the data points. Outliers tend to increase the estimate of residual variance, lowering the chance of rejecting the null hypothesis . They may be due to recording errors, which may be correctable, or they may be due to the Y values not all being sampled from the same population. Apparent outliers may also be due to the Y values being from the same, but nonnormal , population. Outliers may show up clearly in a X-Y scatterplot of the data, as points that do not lie near the general linear trend of the data.