i can comment only to "this answer"
you never know results before testing .
yes model fitted by data from 2009-2017 have better fit over whole dataset.
i guess red model, have "small" coefficient a1 ... y=intercept+a1*x because of that, in 2009-2017 "fit" is above it, its mainly intercept (and because data are moving less).
What is the main question? :-)
edit1. sorry i have to sleep.
but you mention everything right about outlayer impact and R^2 formula too, i guess thats answer to question, to "explaing reasoning"
edit2:
The main question is to evaluate the 2 models and which can be used for forecast the OIS?
- The main question is to evaluate the 2 models
personaly, most simple way of evaluate models, are information criteria like R^2, AIC, RMSE, MAE - Model performance section at http://www.sthda.com/english/articles/38-regression-model-validation/158-regression-model-accuracy-metrics-r-square-aic-bic-cp-and-more/
Alpha for R^2 is usually 0.05= 5% "accuracy", so model is rejected as 0.4391 , considering accepted 0.95 value or higher. As you have only 1 metric for 1 model, you suggests not to use this model because it X doesnt explain Y at appriote alpha. As you dont have data, you can mention metrics (website) and suggest need for them-then you can give more conclusion.
- which can be used for forecast the OIS?
None. Answer is not to using these models (because yellow have poor R^2 and red didnt has been backtested (metrics missing). Period. You can note, from empirical perspective ("method i look i see", sum of abs(residuals)= sum of absolute values of errors.. sum(abs(y-yPredicted))...by eye, it seems yellow model has smaller sum of absolute errors (then) < red model sum...considering criterium/metric "sum of abs errors", yellow model has better performance(lower value) but only with "i see" precission (for higher precision, numbers needed)
But write (collect) everything in this page, because your research/answer should mention all details (imho) :-)
Edit3
why yellow models isnt much bad
according last paragraph at Definitions https://en.wikipedia.org/wiki/Coefficient_of_determination#Definitions
- in the best case, the modeled values exactly match the observed values, which results R^2=1
- A baseline model, which always predicts mean(y) will have R^2=0
- Models that have worse predictions than this baseline will have a negative R^2
Your model have R^2 circa 0.4 which is a much much better then model which predict= mean(y) . It is "bad" model for alpha 0.05. for alpha 0.60 (1-alpha=0.40) it is acceptable model.
Thats why you can suggest not to use yellow model, because for alpha level 0.05% accuracy/precision of model's prediction have "higher error" then 5%..
(take care, information criteria like R^2 has complicated math, i used 5% error to simplify
(imagine you predict bank rate and you have model R^2 = 0.94 .. but customer/manager need alpha=0.01 .. or you have to fill cup with water, cup has capacity 0.5 liter. your hands shaking circa 0.1 liter .. you have high accuracy, but can you repeatly fill cup at 0.45? no, because your error will cause water to go out of cup (wanted 0.45 + 0.1 shaking = 0.55 but capacity was 0.5
yellow model is accepted for alpha 0.6. for alpha 0.5 is rejected.
hehe, but now you can add to your answer, that yellow model outperform "model which predict mean of y".
