By Including Another Variable in the Regression, You Will A Decrease

Short Answer

By including another variable in the regression, you will a. decrease the regression $R ^ { 2 }$ if that variable is important.
b. eliminate the possibility of omitted variable bias from excluding that variable.
c. look at the $t$ -statistic of the coefficient of that variable and include the variable only if the coefficient is statistically significant at the $1 \%$ level.
d. decrease the variance of the estimator of the coefficients of interest.