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I'm fairly new to statistics so pardon me if my question sounds silly. I'm stuck on the conceptual approach to this problem, and any help would be greatly appreciated.

The situation is the following: I have 20 sample batches from a manufacturing process taken throughout different times, at varying intervals, so for example, batch 1 was taken in January 2018, batch 2 was taken in February 2018, batch 3 was taken in May 2018, etc. The performance of each product in each of the batches are measured in a numeric value. In theory, the quality should be consistent throughout time, and there's no reason to suspect the performances of an earlier batch would in any way affect or correlate to the performances in the later batches.

The research question at hand is whether the performances had any statistically significant change (increase or decrease) over time.

My intuition is that the batches are independent of each other, so a simple linear regression should be sufficient for the question, without resorting to time series. There's no good reason to suspect there's omitted variables affecting performance, time should be the only predictor, everything else should remain constant.

My question is whether my intuition is correct, and additionally, if I am correct, how to handle the differences in time interval. Can I just rank the batches 1 through 20, ordered by time, and regress performance on the time ranking?

Thank you for any insights you offer.

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    $\begingroup$ My suggestion is to use "months since January 2018" (which makes the first value for January 2018 equal to zero). If there might be more than one batch in any one month, try "weeks since January 2018" or even "days since January 2018". $\endgroup$ Nov 23 '19 at 0:04
  • $\begingroup$ What do you mean by "without resorting to time series"? $\endgroup$ Nov 23 '19 at 1:11
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It reads to me that you are thinking that you need to treat batch as an ordinal variable. Instead, associate each batch with a numerical time value and perform the regression with this time variable (see @JamesPhillips suggestions in the comments under your post for ideas). The differences in time interval are not a problem when you do it like this.

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