Final answer:
An instrumental variable must be correlated with the explanatory variable (non-zero covariance with x) and uncorrelated with the error term (zero covariance with u) to offer unbiased estimation in regression.
Step-by-step explanation:
An instrumental variable, z, used in regression analysis must satisfy two important conditions:
Firstly, the covariance between the instrumental variable z and the explanatory variable x must be non-zero, implying that z is indeed correlated with x (a). Secondly, the covariance between z and the error term u must be zero, which indicates that z is not related to the errors in the regression equation and provides unbiased estimation (condition c).
Therefore, the correct options are: The covariance between x and z is not equal to zero (condition a). The covariance between u and z is equal to zero (condition c). These requirements ensure a valid and reliable instrument for regression models, providing accurate and efficient estimates of the relationship between the variables.