Yes, this because your linear regression curve has intercept 0.141, if  you put the value of 0.039, the result of X will be negative.Your regression seemed not OK, the value of Y intercept was >>; I think you cannot use this regression curve (especially for low Y'' (

A perfect fit in linear regression (R2=0.99) is nice, but it casts doubt about overfiting - an issue when we use a over discriminated model. I would check how it was derived, and error terms associated to intercept and the regression coeficient. And, of couse, a linear model (y = bx + c) is useful to predict 'y' from 'x'; if you look for the inverse (prediction of 'x' from 'y'), a new model should be derived from original data (it is not an algebra question). 

I don't think so.

what is the values for control?

Send the values to find where is the problem

Hi, in addition I copied from the book of W. Funk et al. 2006; to have good calibration curve the lowest concentration of calibration standard (X1) should be > value of Xa (so it can be proved that X1 is significantly different from zero).

In a regression equation y is the response and x the explanatory variable. That means that to use it, you put in x and get out y, not the other way round. If phenol concentration is your response, call it p, and sample OD what you put in, call it q,  then your regression equation should have been p= a*q + r where r is a constant intercept. So you may need to fit a regression model again, and ensure that you don't try to predict values beyond the ranges that you use to form the model.

The slope and intercept of a straight line in the equation y = m x + c the value of m is called the slope, (or gradient), of the line. It can be positive, negative or zero. Lines with a positive gradient slope upwards, from left to right. Lines with a negative gradient slope downwards from left to right. Lines with a zero gradient are horizontal.

Urvashi  - 

I think that Chris Lee has some papers on his profile that would be helpful for you: 

https://www.researchgate.net/profile/Christopher_Lee24

Cheers - Jim 

Hi, Verma, I agree with Sandro and Miland, you should decide at first which is the explanatory variable and which is the response variable. For a model y=a+bx, it is not correct to find the x-value for a given y-value. In your case, OD at 10µl/ml is the x, and the amount of phenolic content at particular conc. is the y, so you need develop another model, which can not be derived directly from the current model. For some special cases where explanatory variable and response variable can be exchanged, a special technique is needed for parameter estimation. Also, the sample size should be big enough for developing a useful model, and the coefficient of each explanatory variable should be significant, i.e., significantly different from zero. If you need the prediction value to be usefull in practice, it is necessary to define the allowance of some error indices, for example, the mean prediction error (MPE) less than 5% or 10%. Hope it is helpful to you.

Urvashi -

This isn't exactly my area, and that is why I suggested that you check Chris Lee's profile, but isn't your basic problem that your relationship is only approximately linear in a given range, and that it is basically nonlinear overall?   In that case, the intercept for the regression you use would actually be out of range of the real usefulness of that regression. 

Best wishes - Jim  

PS -  See Gunawan's first comments above. 

Correct me if I am wrong, I think your sample's OD is out of range from your standard's equation. Can you show us your data about concentration to make your equation?

Kindly check this link for more explanation about the use R squared http://people.duke.edu/~rnau/rsquared.htm

You wrote … 

"The equation "y=mx+c" for a standard is y= 0.041x+0.141, R2 = 0.995, got by the linear regression equation. In this eq. when I put the value of Y" i.e. my sample OD at 10µl/ml, 0.039,  to find the value of X ( the amount of phenolic content at particular conc.) , the value comes with negative sign.

If the value of x in equation y= mx+c, comes negative, what does it signifies? - ResearchGate. Available from: https://www.researchgate.net/post/If_the_value_of_x_in_equation_y_mx_c_comes_negative_what_does_it_signifies [accessed Aug 25, 2015]."

What this means is that you are have the equation Rs backwards, in some sense.

The equation is a predictor.  By experiment you determine the slope m, and the intercept c, and then with a particular x, you predict y.  

You are doing it all backwards.

Dear Verma

Based on your data you gave, the lowest concentration in your standard gives OD 0.093 which means higher than your samples' OD. Because of that, you can't put that OD on your equation. Your samples' OD must be in range if u want to put it in equation.

What you could do is widening the range of your standard's concentration  or you could add the concentration of your sample.

Please correct me if I am wrong.

Thank you

I just ran a regression model on your data. It suggests that there is a quadratic term in you model. This model is: Conc = -1.344 + 18.79*OD + 2.436*OD^2.

But, the intercept is not significant in this model. So, you can create a model without it. You get: conc = 16.29*OD + 3.365*OD^2. This model shows the when OD is 0.039, conc is 0.6406. That seems to go along with what I would expect. 

It's fairly common for a calibration curve to actually be quadratic or require a Ln transformation. Of the 30 GC based instruments I have used, every single one had a non-linear response. Usually a quadratic term with no intercept worked out best. 

There are a number of problems here, not the least that you are trying to extrapolate beyond the range of the given values. Any such prediction should be treated with caution.

Another problem I see is that the concentration figures look as if they should be the explanatory variable, and you shouldn't be trying to predict them from an OD measurement. Where did the pair (10, 0.039) come from -is this an additional suspect measurement? It seems inconsistent with the data on your spreadsheet. which has (10, 0.607).

Are there scientific reasons to believe that OD should be proportional to the concentration? If so, the intercept can be constrained to be zero.  Otherwise (as Andrew said) you may need a quadratic term in your model. 

My advice is to consult a statistician, and not try to solve the problem by posting questions on Researchgate. I've seen a number of people do this, and they would be better off talking to someone at their institution first, if that is possible.

The slope and intercept of a straight line in the equation y = m x + c the value of m is called the slope, (or gradient), of the line. It can be positive, negative or zero. Lines with a positive gradient slope upwards, from left to right. Lines with a negative gradient slope downwards from left to right. Lines with a zero gradient are horizontal.