Interpreting Regression Coefficients
When I ask you to interpret a regression coefficient, there are several aspects of this interpretation that I will look for.
1. Include variable names related to situation, not just "X," "Y," "dependent," "independent".
2. Include measurement units from the situation, don't just say "units".
3. Correct direction of influence or effect. The unit increase in X precedes or "leads to a predictable" change in Y.
4. Associate the magnitude of the regression coefficient () with the change in the dependent variable that results from the unit increase in the independent variable, X.  This magnitude does not tell you how much X changes.   X always increases by one unit to get Y to change by  units. The sign associated with  tells us whether Y increases or decreases by  units when X increases by one unit. (If you begin your interpretation with a unit decrease in X, then remember to reverse the direction indicated by the sign when you describe the change in Y.)

    Note:    A positive coefficient means X and Y change in the same direction.  If X increases, then Y increases.  If X
                decreases, then Y decreases.  A negative coefficient means X and Y change in opposite directions.  If X
                increases, then Y decreases.  If X decreases, then Y increases.
5. The regression coefficient is  not . Excel calls them both coefficients, but we will be concerned and talking about . We will call  the intercept or constant.
6. Remember that we are talking about changes in X and changes in Y, not levels of either. This is like the idea of a marginal change in your economics classes.