# How to find the relationship between an independent variable in a time series and a single dependent variable

I have a dataset of crop yield of a seasonal crop, under environmental conditions (rainfall, humidity, temperature etc.). Daily environmental conditions are recorded over few years with the crop yield of each season.

example:

Date , Temperature , Humidity , Rainfall

1/31/2019 , 28 , 64.55 , 1.2

2/1/2019 , 28.2 , 65.81 , 1.2

2/2/2019 , 28 , 67.18 , 0.6

2/3/2019 , 28 , 68.54 , 0.4

2/4/2019 , 27.43 , 69.17 , 0.2

Crop yield for the above season is 37000kg.

Can you guide me on how can I find the relationships between the crop yield (dependent) and each environment factor (independent)? I am trying to find the impact of each factor on the crop yield of a season but I am having a hard time figuring out how to find correlation between a time series (environment factor) and a single variable (crop yield).

• Search online the words "Multiple linear regression" and go from there. May 10, 2020 at 1:11

Have you tried fitting the data using a method of least squares linear regression approach for different forms of equations? This would help eliminate what form the equations take? If you are having trouble with this, I could share some good examples from a book I am presently learning from "Engineering Mathematics - K A Stroud"

You are trying to find the correlation between multiple time series to a single variable. Now, a key point is that this single variable is affected over time because of the effects of the different environmental conditions. So, the effects of the time series of the conditions is another time series perhaps daily crop yield. One could think of the single variable as the integral or the summation of the this hidden time series.

There are many different ways to estimate an unknown series and it is unclear which would be appropriate because you only know the sum of the series. Hidden Markov models and Filtering methods like 3d-var are possibilities to try out but there might be better methods.