we call this type of data arima chart. the input depends on output. you could use more tools to study it, in essence its important the independent variable becomes independent of other variable, not really of Y. u can use acf charts to use the autoregression data. good day

To answer your question, you must understand what a covariate does and does not do in a regression (or ANOVA). The way that a covariate increases the precision of an analysis is by reducing the unexplained within group variation. What you are suggesting may, indeed, decrease the variation across the independent variables since it is draw from the independent variable. This could counterbalance any benefit derived from using a covariate. It is also important to know that a covariate will not correct appropriately for across group differences. The only way you can know the answer to your question for sure is to run it both ways and to compare the effect size of the independent variable with and without the covariate (R squared with and without the covariate). I am not sure this paper would answer all of your question, but you could learn more about covariates by reading "The Care and Feeding of ANCOVA," a paper available on Researchgate by me. Good luck!

Let me state the problem you have as

X independent variable and Y dependent variable

Y: Nighttime lights raster

X: Population raster

Based on the data (xi, yi) for i=1,….,N wish to fit a model for Y=a+bX+e

Let this data related to Location 1 ( which is of your interest) Say D1 ={(xi,yi)|i=1,2,…}

Let you have a sicario say other Location (Source) - data set from location be D2={(uj,vj)|j=1,….}

U: Nighttime lights raster at other location (Source)

V: Population raster at other location (Source)

D3 be an historical data of the Location 1

D4 be an historical data of the Location 2.

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Let Z2 be simply a function of Y say Z2=g(Y)

One should not attempt Y on Z2

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If Z2 forecast for Y then one can try Y on Z2

Model1: Y=a+bX+e

Model2: Y=a1+b1*Z1+e Z1 is a derived variable

Case i: Z1=b0+b1*X+b2*U+b3*V+e a linear model for Y based on the historical data D3 and D4.

Case ii: Z1=b0+b1*X +e a linear model built for Y based on D3 alone

Case iii: Z1 = forecast of Y based on D1 ( auto regressive with covariate X, U and V with apt lag)

Mode 3: Y=b0+b1*X+b2*U+b3*U+b4*Z1+e