This thesis presents inference for the multiple linear regression model Y = beta_1 x_1 + ... + beta_p x_p + e after model or variable selection, including prediction intervals for a future value of the response variable Y_f, and testing hypotheses with the bootstrap. If n is the sample size, most results are for n/p large, but prediction intervals are developed that may increase in average length slowly as p increases for fixed n if the model is sparse: k predictors have nonzero coefficients beta_i where n/k is large.