The bootstrap is a computer based resampling procedure for estimating the correct variance of an estimator directly from the data obtained rather than from assumptions on the underlying error distribution. The objective of the research is to study the bias associated with the bootstrap and to consider several alternative procedures for correcting this bias. This is accomplished via an extensive Monte Carlo simulation study in the linear regression context. This simulation involves a range of underlying error distributions, a variety of structures for the design matrix, and a range of sample sizes. Three new corrections for the bias in estimation of the variance are considered, and a significant contribution of this research is that one of these is demonstrated to be an improvement over the usual Bickel and Freedman's correction. The remaining two are demonstrated to be less desirable, these are based on an inner/outer loop bootstrap procedure