State whether the following statements are true, false, or uncertain. Give your reasons. Be precise.
a. The stochastic error term ui and the residual term ei mean the same thing.
b. The PRF gives the value of the dependent variable corresponding to each value of the independent variable.
c. A linear regression model means a model linear in the variables.
d. In the linear regression model the explanatory variable is the cause and the dependent variable is the effect.
e. The conditional and unconditional mean of a random variable are the same thing.
f. In Eq. (2.2) the regression coefficients, the B's, are random variables, whereas the b's in Eq. (2.4) are the parameters.
g. In Eq. (2.1) the slope coefficient B2measures the slope of Y per unit change in X.
h. In practice, the two-variable regression model is useless because the behavior of a dependent variable can never be explained by a single explanatory variable.
i. The sum of the deviation of a random variable from its mean value is always equal to zero.