I have the following model;
log(daily sales) = intercept + B1*(event dummy) + error
My response variable(daily sales) is basically a daily time series and 'event dummy' is an indicator variable whose value is 1 when a certain event is ON and 0 when OFF.
I have the value of B1 now; say, 0.3. This means that the mean daily sales is multiplied by exp(0.3) as the event dummy gets bigger by 1 unit.
But I have to convert this multiplicative effect into some 'absolute effect' in daily sales. Which is correct among the following suggestions? Or are there any other solution that is more appropriate?
- (exp(0.3) - 1) * mean daily sales when event dummy is 0
- ( (exp(0.3) - 1) / exp(0.3) ) * mean daily sales when event dummy is 1
[explanation for the 1st approach] (exp(0.3) - 1) is the growth rate corresponding to 1 unit increase in event dummy. But this 'growth' means the 'growth compared to the mean daily sales when the event is OFF', so the formula came out.
[explanation for the 2nd approach] Likewise, (exp(0.3) - 1) is the growth rate corresponding to 1 unit increase in event dummy. Then, 'mean daily sales when the event is ON' is actually the mean daily sales AFTER the multiplicative effect has taken place. So we have to re-construct the mean daily sales IF the effect wasn't there, and examine the difference between the two. So the formula came out.