# How to calculate a regression based on the data having a correlation?

I have continuous data changing exposure to the object. And the data of the response object to the impact measured at two points. I need to build a regression line of the response object.

When measuring the reactions at two points, obviously video passing through them. But I want to improve the predictions, using data effect.

Example ==========================================================

These impacts are:
1 = 169,10%
2 = 150,65%
3 = 134,22%
4 = 119,57%
5 = 106,53%
6 = 94,91%
7 = 84,55%

Measurements of the reactions at points 1 and 4: of 0.37 and 0.12

How to calculate the response at other points, most accurately if I know that impacts in 169,10% gives the reaction of 0.37, and the impact of 119% ~ 0,12 ?

The problem is that the exposure data, I can roughly calculate a measurement of the reaction a very expensive operation. Literally.

UPD:
Some clarification:

1 actually points of measurement, not two, but three - the third hypothetical - I know that at zero exposure, the reaction of 0.05. In General, you can deduct a basic level of response and to say that 0 == 0; 169 == 0,32; 119 == 0,07, X == ?

2 of course, I just tried to build the line, taking over one of the axes of vozdeistvie - in principle, such a curve passes through both points of the experiment shaped curve effect. But for these values goes negative already at about 60% of the impact that nonuse. The reaction cannot physically be negative.
April 7th 20 at 15:44
April 7th 20 at 15:46

The equation of the line through two given points "1" and "4". Lead to the form `y = f(x)`
The resulting equation for X to convey effects and to forecast reactions of Y.
I know about the line through the two points. Here are just a nichrome dependence is not linear, this time, the impact of the change is also not linear, that's two. And I want to get as close as possible aproximarse curve.

Speaking geometrically on the fingers, I want to straighten the curve of the exposure so that it passes through points of the reaction. - Erich.Ratke commented on April 7th 20 at 15:49
@lexus, the numbers of the experiments 1..7 have some sense not specified in the question?
Maybe they go through equal intervals (of what?)

Now the question describes only two parameters: the exposure X and response Y. And Y is known only for two points. Through them you can only hold one straight line and an infinite number of curves, which no longer has any data at all. - fermin_Schneider14 commented on April 7th 20 at 15:52
here is what we have now
- fermin_Schneider14 commented on April 7th 20 at 15:55
@Destini.Beier, I thought it meant - Yes, of course the numbers of experiments are at equal intervals of time - in this case day, but actually I have a forcing function and I just can calculate any point.

The red line can be ignored. Blue - what I say is just force over time.
Experiments 1 and 4 the results of the system response. - Erich.Ratke commented on April 7th 20 at 15:58
April 7th 20 at 15:48

Choose any curve, they all pass through your two points.
Want more or earn additional points or build a model for determining the equation based on feedback from vozdeistviyu
Proupdater question. In fact, points three and I know that there is a correlation between exposure and reaction, because the curves in images is not exactly suitable, as less impact gives less reaction always. Form of reaction curve should follow the shape of the curve effect. - Erich.Ratke commented on April 7th 20 at 15:51
@lexus, and the three points can be made arbitrary number of curves. It is necessary to know at least the General formula based on feedback from exposure.
A correlation is simply a statistical correlation of random variables. It does not mean dependence of one magnitude from another. For example, the damage from a fire has a positive correlation with the number of firefighters to travel to its suppression. But this does not mean that if you don't send firefighters to extinguish the fire, the damage will be reduced or if you send several times more fire, the damage will increase. - Philip83 commented on April 7th 20 at 15:54
@soledad98, no, no - in this case, we know that there is a causal link.
We are talking about a chemical reaction.
Control action (predictor) in this case is the introduction into the environment of chemical compounds, which catalyzes the process.
Reaction - the release of nutrients.
There is a basic level of output, without the use katalizatorov, and it is less than 0.05 (we don't know more exactly), but assume in the area of 0,03~0,04

We know that when the catalyst in a 169% gain yield of 0.37
Want to build a curve at least roughly showing the dependence of the yield from - Erich.Ratke commented on April 7th 20 at 15:57
@lexus, Chemistry - it is dark. IMHO, there are too many settings to bind only to the amount of the catalyst. For good, you have to study the formula of the reaction, to see how it is activated catalyst. Maybe there will asymptote, and maybe with further increase of the amount of catalyst the yield will start to decrease. But it's all rather a question for the chemical forum. - Philip83 commented on April 7th 20 at 16:00
@soledad98, yeah, yeah, I know. This is why make measurements of the output and trying to build a chart based on experimental data, for a start at least some.
We can precisely regulate its supply.

Even worse, there are two limitations: - we can make measurements only 12 hours after entering the catalyst, when it know that its action develops immediately.
Even worse - catalyst two.

The blue line is K1, the values of which I led, and the red is K2.
Yellow tags - the measurements of the output.
Now I'm trying to build a line that can support K1 in the range from 1 to 110. - Erich.Ratke commented on April 7th 20 at 16:03
@lexus, If I still forgot from school chemistry course, the catalyst by definition can not be consumed in the reaction.
You have two options. The first is experimental, it is necessary to obtain many points by which to assess dependency. The second - analytical, it is necessary to obtain a General formula based on the theory/model, then using multiple points to determine the coefficients in this formula.
Now the data is not enough to select any specific formula.
And when the two catalysts are also possible synergies when their combined effect differs from the simple sum of the actions of each of them.

P. S. I Can assume that the graph of will have two asymptotes - near zero and at the maximum, and a linear plot in the middle. But on two points of such a graph is not parameterized.

P. P. S. Although, maybe something like volt-ampere characteristics of the transistor, with a single upper asymptote. - Philip83 commented on April 7th 20 at 16:06
If I have not all forgotten from school chemistry course, the catalyst by definition can not be consumed in the reaction.

All right because it's not really a catalyst. I'm trying to explain the process as short as possible. I don't have opportunities and challenges to describe the entire physics of the system. The simple - to imagine that it is the catalyst that is still consumed.

The first is an experimental, we need to get lots of points by which to assess dependency.

Well, suppose I already have 3 points. It's a lot or not? If I can't solve the problem at least three points, at least very roughly, the 30 I little help.

The second - analytical, it is necessary to obtain a General formula based on the theory/model, then using multiple points to determine the coefficients in this formula.

Escuchen.

And when the two catalysts are also possible synergies when their combined effect differs from the simple sum of the actions of each of them.

Yes. Moreover, we know that this synergy is.
The challenge now is to establish the relationship for K1 and collect data for K1+K2 then, we deduce K1 from the process and get the data only for K2. - Erich.Ratke commented on April 7th 20 at 16:09
@lexus, If you don't have any idea about a possible formula, then three points is obviously not enough. Given that there are dealing with a real process, the schedule can be piecewise continuous, for example up to a certain concentration of output increases linearly, and then, as saturation becomes an asymptote, or first log grows to the maximum, then starts to fall exponentially.

Thirty points may be sufficient for the overall assessment, if they are more or less evenly fall on the region definitions and function values. If all these points are below the mid-region of the definition, there is nothing about the behavior of the function above means to say without knowledge of the theory (mechanics, chemistry, physics) process. - Philip83 commented on April 7th 20 at 16:12
the schedule can be piecewise continuous, for example up to a certain concentration of output increases linearly, and then, as saturation becomes an asymptote

Probably true by the way. We have data of other groups, but they had a different method of measuring the exit (which we don't like, but they have more measurement points) and of course they have a different instance of a system which is also affected.
And we think over the increase of measuring points and the offset points to the extremes of exposure, but this will only be possible in summer or even autumn.
And now there is a task to achieve the most smooth exit, using the data that is already there and the combination of the catalysts (the point is that the blue is about 6 times more expensive, and use a red permanent, otherwise will need to stop for measures for removal of decay products) to stabilize the system.
If our (or any other) chemists could theoretically calculate, that would just be happiness.
PS
I really only do collection and visualization of statistics, but I want to help so to speak. - Erich.Ratke commented on April 7th 20 at 16:15

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