Dear Dhritikesh;

If only reality is the field with X,Y,Z and time, 4 dimension is enough.

I do not recognize all matter is real and is all state or phase of

only vibration with fine mass in/of the field.

Kazuo Oie

Your question is really poorly written. If you want to know if observations follow a linear law, one easy way is by graphing them and trying to fit a straight line to them. So simple. Taught in your early school days.

The observation is a very intimate and dynamic process. It depends on space (-remoteness), on time(-willingness) and on value(-awareness).

A simple example:

Take 10 people reading the same book. Check what they understood out of it.

Take a book you did read 10 times. Why do you observe every time different things?

Stream your conclusions with other people that had the same experience. How does the streaming affect what you already observed?

Interesting questions. But this is a website for science, and you must think like a scientist, even if you are clearly not trained as one. Consider how your questions could be answered on objective grounds, using reliable experiments that produce measurements. And don't do it here, with me. We mustn't abuse this forum, which is for scientists.

Do this planning on your own, and consult your teachers to find out if you are correct. Experiments, especially on human subjects, are not easy to design. Read a book or a tutorial on the subject of experimental design. And don't assume that anything involving humans will be reproducible or linear in nature. And expect both your experimental design and the experiments themselves to take a long time, if you wish reliable or quality results.

Dear all;

Here, ResachGate is platform for scientists on objective grounds、but here is also researchers on philosophy as well as cognitive science. Of course we must take care for we are objective and/or subjective. But how about principle of uncertaintity? Where our accuracy high enough to observe objects, their existents themselves become obscure.

I myself is welcome to such a discussion, because some patients have just existential problems and special approach might be required and effective to get remission, which mean they become adjusted to his/her family, school or workspace.

Cf.

Frankl’s existential analysis

J.P. Sartre’s existentialism

Sincerely yours,

Kazuo Oie

Kazuo Oie , Of course you are absolutely correct about Research Gate. However, this questioner mentioned "linear model" which is a term from statistics and is not uncertain.

Dear readers;

Dhritikesh question might be just one of statistics、but may be not.

As you know, DNA has exons and introns, transcripted to mRNA and not. mRNA is translated to amino acid sequence and further, proteins. But as far as I know, 100% acculate grammer to find boundary between exon and intron tried to read just DNA sequence level, I mean triplet codon level. DNA is read by intracellular structure with higher order one.

I think Dhritikesh might want ask there is such uncertainty or not.

Am I correct?

By the way, drugs are powerful and useful with such a higher order structure, but as well as the cause of side effects.

Kazuo Oie

I have gone through the answers given by Kazuo Oie , David Spector and Anamaria Popescu. Thanks to them for their answers.

I like to clarify my question.

Here, X and Y are two variables following the linear model

Y = a + bX

where a & b are the parameters.

Y1 , Y2 , Y3 , .................. , Yn

are the observed values of Y corresponding to the observed values

X1 , X2 , X3 , ................... , Xn of X.

The observations (i.e. the observed values) are not free from error.

This means that each of the observed values is composed of the true/actual value and error. Now, the two variables X and Y follow the above linear model implies that the true/actual part of each of the observed values follow the linear model.

Since each of the observed values contain two components namely true value and error therefore each of the observed values is different from the true/actual value. Therefore, it is a question whether the observed values follow the linear model. My thrust is to know what model is followed by the observed values of X and Y .

If the observed values do not fit into your linear model, then they are not linear. The excursions from a least-squares-fit line indicate the degree to which they are not linear. This is standard elementary statistics and is described in detail in any elementary statistics textbook.

@ David Spector , If the observed values fit into the linear model, then they are linear. However, this linearity is not exact but approximate (may be the best approximate) i.e. all the data points do not lie on the fitted line but lie at distances (may be minimum) from the line. Accordingly, the given data do not follow the linear model perfectly.

My thrust is to know about the perfect model followed by the data set.

I'm not sure what your misunderstanding is. I tried to make my answers very clear. This material is covered in any elementary textbook on statistics, so please locate one and read it instead of asking the same question again and again here.

I have not found what is my misunderstanding and where I am wrong.

I am sorry that you are having trouble understanding how to calculate to what degree your measurements depart from a linear model. As I said, this is basic statistics, explained clearly in textbooks, so it is not a subject for posting in a forum. I'm not a statistics teacher, and it's been a long time since I studied statistics, so I cannot teach you what you need. Read and study a textbook, as you did when you went to school, so you have the knowledge you need. I wish you the best of luck.

I have understood the problem as follows:

If X and Y are two variables following the linear model

Y = a + bX

where a & b are the parametersand if

(X1 , Y1) , (X2 , Y2) , (X3 , Y3) , ................... , (Xn , Yn)

are observed values on the variables X and Y

then it is natural that the observations are not free from error.

Thus, each of the observations are composed of actual value and error.

In this case, my view is that if the error is insignificant then the observations can be treated to follow the above linear model statistically but not mathematically. Because, insignificant error does not mean zero error.

In order to follow the linear model by the observations mathematically, the error must be zero.

In order to follow the linear model by the observations statistically, the error need not necessarily be zero but necessary to be insignificant.

I beg to request all to give comment(s) on my view.

Dear Dhritikesh Chakrabarty ,

Mathematical modeling is the best way to describe many (dynamical) situations in our life; this will provide approximate values rather than the exact values.

If we have a massive number of data, it is not practical to show them all, and this will help to save time and efforts.

So It is better to provide a candidate algorithm (formula) that present the whole list of data, of course, it is not the exact real values, but it is very close to the real ones, where the margin of error is accepted.

So, in each type of data, we have different suggestions to choose the best algorithm, and the statisticians prefer different curves according to the nature and the kind of data.

In your case, you confirmed that the available data are linear; that is, the data were distributed and accumulated around a line.

If all data are collinear, then the least square fitting provides exact values.

But in general, this is not the case, that is the data represents non-collinear points; hence the generated coefficients a and b ( By least square fitting) represents an approximation which minimizes the errors.

So, the problem is elementary, as mentioned by many other followers.

Best regards

Dear Issam Kaddoura ,

The mathematical modelling, the least squares method the the other available statistical methods can yield the values only, of the parameters a & b, which may not be free from error though the errors involved there may be small. My thrust is to determine the values, of the parameters a & b, which are free from error.

Dear Dhritikesh Chakrabarty ,

If the data represent noncollinear points, we can't find exact values for a and b

that fit the curve y = ax + b .

Only optimum values can be determined.