Hypothesis testing in the linear regression model is a fundamental statistical problem. We consider linear regression in the high-dimensional regime where the number of parameters exceeds the number of samples and assume that the high-dimensional parameters vector is sparse. We develop a general and flexible projection statistic for hypothesis testing in this model. Our framework encompasses testing whether the parameter lies in a convex cone, testing the signal strength, testing arbitrary functionals of the parameter, and testing adaptive hypothesis. Our numerical experiments confirms our theoretical findings and demonstrate that we control false positive rate (type I error) near the nominal level, and have high power.