This thesis introduces a new specification test for models in regression analysis, testing if the error terms of a regression model have expected value of zero conditional on an explanatory variable H0 : E[U|x] = 0. Two versions of the test are developed: the Basic Test assumes that one can observe the real error terms serving as a foundation for the development of the second version of the test, the Feasible Test, which works with residuals from the fitted model. The test is performed by calculating a matrix W from which the test-statistic v = uTWu can be calculated. Under the null hypothesis the v-statistic will follow a generalized chi-square distribution with the eigenvalues of the W-matrix. Towards the end of the thesis the test is compared with Ramsey’s RESET Test which also is able to test the null hypothesis H0 : E[U|x] = 0 but in a different way.