Testing the influence of Time Period on Y I am trying to measure the decay in the rate of sales from period one, to period two, to period three, to period four. My sample data structure looks like this:
Product Sales Period X1 X2 X3 
A       140    1     (omitted)
A       130    2
A       90     3
A       70     4
B       100    1
B       95     2
B       80     3
B       74     4
C       111    1
C       100    2
C       60     3
C       40     4

What I did, was estimating an OLS by regressing Sales on Period as a categorical variable (and a collection of other independent variables). 
Period |        coeff       stdev        t      p-value   
          2  |  -.043726    .0155788    -2.81   0.005    -.0742619   -.0131901
          3  |  -.0212789   .0155709    -1.37   0.172    -.0517993    .0092415
          4  |  -.0156485   .0155811    -1.00   0.315    -.0461889    .0148918

However, I realized that this might not be a correct approach given that I essentially treat periods as simply independent values without accounting for the time component (1 goes before 2, 2 goes before 3, etc.). 
Can you suggest another way of measuring this so-called "decay rate" based on a period? 
 A: Fitting a trend line (or any polynomial in time) as you are doing (sales on period) is based upon a model assumption which should studiously avoided be voided UNLESS the residuals from such a model are free of any structure ( such as memory , pulses , level or trend shifts , or changes in error variance over time (period) ). Modern analysis suggests forming a possible hybrid model containing memory (ARIMA) and any needed dummy variables to account for pulses , level or trend shifts . Upon obtaining a model that can be statistically verified to be sufficient the next step is to somehow "label the model". The correct label might be a constant decay from period to period or a constant change from period to period or an auto-regressive dependency from period to period. Now the good news is all models developed in this way can be characterized as "weighted average of previous values" where the number of periods and the weights themselves (most likely unequal !) are presented.
Often time there may be too few observations to empirically form a unique model for each series. In this case some (professional) judgement may be needed to apply a common model form to all series .
