Consider the following regression model:

We are given a two variable regression model, with explanatory variables X1 and X2 and dependent variable Y. We are estimating the model with a constant term, so we have three parameters, B0, B1 and B2.

1. Given we have obtained an estimated value of B1, i.e. B1 (hat). Statistical significance and economic significance are two concepts which differ from each other, but must be utilized together to understand the overall significance of the parameters. Economic significance is determined by whether the value of the parameter fits with the underlying economic theory or not, i.e. if it has the correct sign or not and similar concerns. For e.g. if we are estimating a regression of quantity demanded of a product with price as an explanatory variable, we would expect the parameter to have a negative sign in line with the law of demand. Statistical signficance, on the other hand, simply concerns whether the estimated parameter is significantly different from 0 or not. This can be estimated through the t-value or p-value approach, by testing the hypothesis of B1=0. If the null hypothesis is rejected, the parameter is said to be statistically significant. Statistical significane is not concerned with economic significance, and simply states that the parameter estimated has a signficant impact on the dependent variable. It does not specify whether the impact is in line with economic theory. Hence, both statistical and economic signficance should be evaluated when estimating a regression model.

2. B1 and B2 represent partial slope coefficients, since there are multiple variables in the model. B1, for instance, measures the change in the dependent variable Y as a result of a unit change in X1, keeping all other factors (in this case X2) constant. If B1 = 0.7, a 1 unit change in X1 will result in a 0.7 unit change in Y, if X2 is held constant. The same reasoning applies to B2 as well. This 'holding other explanatory variables constant' makes B1 and B2 partial slopes.