Exponential regression of data close to one

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The discussion centers on the challenges of using exponential regression to model sales data, particularly for products with low sales figures. The initial confusion arose from the integration of the model, which seemed to inaccurately predict sales for products with sales close to zero or one. The issue was identified as a programming error where data points for time periods with no sales were not included, leading to inflated predictions. Once the code was corrected to account for these zero sales, the model began to function as expected. This highlights the importance of accurately representing all data points in regression models for reliable predictions.
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Hi,

I've been working on trying to model sales for my work and I'm really just modeling it using exponential regression, so I get the linear regression of the logarithm of the data and obtain the desired formula.

What I'm confused about is that if I integrate this to try to predict how many sales will be from now to some future point, it seems to work OK for products which have more sales (sale numbers are far from 1 for a given period of time) but not so well for products with poor sales (sales numbers that are either 0 or ~1 for a given period of time).

For the latter products the exponential model seems to predict that there are on average around 1 sale per unit of time, which when integrated ends up adding together a bunch of 1's for each period of time.

Am I misusing exponential regression or is this a limitation of its use?

Many thanks!
 
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Hi !
I cannot fully understand what is the problem. can you post an example of data ?
 
Thanks for the reply! But actually it turned out to be some sort of programming glitch. My first huge mistake was to not add in data points for time periods that had no sales. I realized this and wrote the code to add in zeroes for these, but when I was still getting expected values that were well over the actual ones, I thought maybe my model was screwed up.

Apparently the error affected slow selling products more because they tend to have more time periods with zero sales. But anyway, the code randomly started working as expected so no complaints.
 
Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

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