Regression model for lifetime data is considered, in which the underlying distribution is extreme value where the effect of the regressor variables on the mean is assumed to have linear representation. A new technique is proposed for estimating the regression coefficients by maximum likelihood (ML) method and moment properties with bias approximation of these estimators are examined theoretically and assessed by Monte-Carlo simulation for the case of a single explanatory variable. The properties of various confidence intervals for these estimators are developed with bias correction. Finally we consider hypothesis testing procedure concern the effectiveness of a subset of the explanatory variables and an approximation to the distribution of a test statistic is mathematically derived and studied practically.