# Interpreting Linear Model Coefficients with Lagged Variables

Let's say I have a data set which looks like below and I'm running a linear model to predict income on two predictors.

date    date-1    income   region    age
mar       apr      50        2        55
apr       may      10        3        40
may       jun      35        1        35
....

Income = B0 + B1(Region) + B2(Age)

Let's say that I get the following coefficients from the model. How would I interpret such results.

Est
Intercept    130
Region       0.05
Age          0.10

So with a one month lag, how would I go about interpreting this model. What if it were a two month lag?

• Please write the regression specification using mathematical notation and not computer language -a lot is missing, for example it is not clear the lags of what variable(s) are included in the regression. So: mathematical notation. Also you must specify the units in which each variable (dependent and regressors) is measured. – Alecos Papadopoulos Sep 27 '13 at 19:45

If [Income at date] = B0 + B1[Region at date-1] + B2[Age at date-1], then the fact that you are using data from a month ago to forecast Income this month is only saying that this future income value is predictable. The same is true if the lag is changed to two months.

If on the other hand, you had [Income at date] = B0 + B1[Region at date-1] + B2[Age at date-1] + B3[Income at date-1] where we have added a third predictor which is the same as the dependent variable but lagged, then we are looking at time series modeling, more specifically autoregressive moving average (ARMA) models.