filling data gaps in time series using multiple linear regression

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Hello,
I have multiple rain stations in a catchemnt. I choose 3 of them which are close to eachother. I have 10 years of data from each station, but all 3 times series have data gaps.
I choose 3 years of data without gaps (minor 1 or 2 days gap) within the time series to find the correlation as below.
Then I did Multiple Linear regression as shown below.
Questions.
1) Is this the write procedure fo fill data gaps in time sereis using Multiple Linear Regession (MLR).?
2) stats have 6 values. Kindly help me understanding what every value means.(If it was 1x4 then I know it is R-squared, F-stats, p , signfance).
3) when I used the equation and picked random value to find the predicted value y(which I know from time series) it is 0.4 and predicted value is 5.6.
4) If I have really strong correlation coefficient why predicted value is not so close?
Any help would be appreciated.
Thanking you in advance
  16 Comments
dpb
dpb on 14 Nov 2021
Again, the effectiveness of this model will be highly dependent upon the type of rainfall event your particular catchment sees. If it is, indeed true that "when it rains, it rains" over a large area, then it will likely be a fairly representative surrogate. If it's AZ or SW KS, I'd venture "not so much".
I wholeheartedly agree with @Dave B that visualization should be a key component of exploratory model-building and verification; simply relying on blind correlation is not science.
Muhammad Haris Siddiqui
Muhammad Haris Siddiqui on 15 Nov 2021
@Dave B @dpb I agree with both of you. Thank you for you time and effort you put in this problem.
Indeed, it is a valuable discussion.

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