Please help to improve graph formula

[Tomcater]

Hello everyone,

I have a graph.
The blue line created from measured values.
All over created from calculated values obtained from 3 different sources.
The red line is the best.
The gray one is ok.
The yellow on is ok in the middle, but the first and the last points are not good. Because of that, I have to drop this line and its good values from the graph.
The point is to create a combined line from all the calculated values which must be as close to measured values as possible.
So, would you mind to advice how can I adjust the yellow line formula using other lines formulas? I would like to make these 2 points closer to the blue line.

Thank you!

 

[tkhunny]

You may wish to consider a "Least Squares" approach. Is this in your realm of experience?

 

[stapel]

I have a graph.
The blue line created from measured values.
All over created from calculated values obtained from 3 different sources.

What does "all over created" mean? How do the values from "3 difference sources" differ from the "measured" values?

The red line is the best.
The gray one is ok.

What does this mean? If the red line is not based on actual values, in what manner is it "the best"? How were the red and gray lines derived? In what sense is the gray line "ok"?

The yellow on is ok in the middle, but the first and the last points are not good.

What was the source of these points? In what sense are the "not good"?

Because of that, I have to drop this line and its good values from the graph.

Why? Under what rules are you operating?

The point is to create a combined line from all the calculated values which must be as close to measured values as possible.

How has your textbook or your class instructor defined this "line combination" process? What, exactly, are you meant to be doing?

When you reply, please include the full and exact text of the exercise, the complete instructions, and all other information (such as the data points they've given you, along with the other stuff [red, blue, yellow, whatever]), as well as how this question arose in your calculus class (that is, what topic in calculus generated what appears to be a statistics exercise). Also, please provide a clear statement of your thoughts and efforts so far, which should greatly help us with understanding what it is that you're trying to accomplish. Thank you!

 

[Tomcater]

Good morning, friends
Thank you for answers!
I'll try to explain what I have to do.
The topic is to define a crop coefficient parameter called Kc that uses in the crop irrigation process.
The blue line is the parameter actually measured during the field experiment.
All over lines - are calculated Kc from different sources.
The obtaining formulas I use Values as Axis x, Kc Measured as y, and KcEstimated is the result of values multiplied on the formula I've got.
The red line - is a very good model derived on results of optical satellite sensing. This model based on next points:

Date Values Kc Measured KcEst 20160715 4.1153 0.9104 0.9062 20160725 4.0776 0.9025 0.8986 20160804 3.887 0.8448 0.8598 20160814 3.5538 0.7994 0.7921 20160824 2.9854 0.6756 0.6765 It has KcEst=0.2033x+0.0696 (R2=0.9915) formula to transform its values to the Kc Estimated.

The next line is a gray line. The values here obtained from the images taken by a radar satellite during certain type of orbit
The model based on the next points:

Date Sensing Values KcMeasured KcEstimated 8-Jul-16 0.2502 0.7998 0.8339 20-Jul-16 0.2437 0.9183 0.8995 1-Aug-16 0.2578 0.8898 0.7568 13-Aug-16 0.2434 0.8552 0.9030 25-Aug-16 0.2687 0.5729 0.6463 6-Sep-16 0.2918 0.4164 0.4130

The formula is KcEst=-10.129x+3.3684 (R2=0.868)

And the last one is the yellow line. Values here were also got from the same radar satellite, but from the different type of orbit

Date Sensing	Values	KcMeasured	KcEst
4-Jul-16	0.2308	0.8385	0.5426
16-Jul-16	0.2409	0.8642	0.9294
28-Jul-16	0.2393	0.9283	0.8688
9-Aug-16	0.2392	0.8847	0.8646
21-Aug-16	0.2342	0.7050	0.6720
2-Sep-16	0.2321	0.4824	0.5922
14-Sep-16	0.2307	0.3068	0.5407

The formula is KcEst=38.435x-8.3281 (R2=0.5081). Without points from the Independence Day and September,14 the R2 would be much higher.

All the models based on the different days and my task is to create a combined model which would have all points from all the models. This model must be used for circumstances when we wouldn't have the measured data. I would like to use all points from all the models, but each estimated point must lay not far than 0.1 or 0.2 from measured. Most of the points of the gray model are good, but if I will not know the measured values I will not be able to trust to this model at all because I know that some of the points might let me down.
So, my question is what I have to do in the situation if I know only values from each type of the models, how can I interpolate results from other models to the gray model to prevent it from having points lay very far from the places where them supposed to be.

Thank you!