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12-02-2014 06:33 AM

Hello everyone,

I have situation in simple linear regression where is: max. value of Y variable (a*) = 3,31

min. value of Y variable = - 0,85

max. value of X variable (pH) = 6,56

max. value of X variable = 6,28

their mutual change is shown in picture 1.

After that, i get regress. equation: - 95,37 + 15,03*(pH)

For prediction, the equation is ok , but for interpretation of the results, those coefficients are 10 time bigger (and tottaly unrealistic) then interval of my data....My question is whether I can for discussion say: Y differs 1,503 units for every 0,1 unit difference in X...

Tnx,

Tomislav

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Solution

12-02-2014
03:58 PM

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12-02-2014 03:58 PM

The strait line provides a reasonable fit to your data. In most situations, a change of one pH unit is a major change. Just use as a unit what is useful for interpretation in your field. Don't forget that the center of the pH scale is around 7 for most people, thus the magnitude of the intercept (i.e. zero is very far away).

PG

PG

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12-02-2014 10:21 AM

The size of the coefficients depends on the slope and intercept, and does not depend on the "interval of my data".

So, I don't see the problem.

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12-02-2014 10:33 AM

I know that the size of the coefficients depends on the slope and intercept, but that was not my question

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12-02-2014 10:56 AM

I believe what you said is how one would interpret such a coefficient, presuming analytical assumptions were met, and your graph appears to confirm that.

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12-02-2014 11:15 AM

Hi Arthur,

I wanted to know if there is a possibility (in paper discussion) to say: Y differs 1,503 units for every 0,1 unit difference in X, than (classical) Y differs 15,03 units for every 1 unit difference in X. In results section, equation will still be Y(pred.) = - 95,37 + 15,03*(pH).

(I ask this because theoretical background of my field)..

Tnx,

Tomislav

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12-02-2014 12:01 PM

I'm not a statistician but, if you multiply the dependent and independent variable by the same amount (in this case .1), the intercept would change to its current value*.1, and the coefficient would remain the same.

Thus, if you are going to report it in those terms, you probably should show the graph and equation in those terms as well. As for the the theoretical background in your field, though, I wouldn't differ from what your colleagues are used to seeing.

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12-02-2014 12:23 PM

Check the model assumptions, normality of errors etc.

pH is on the log scale so sometimes making a transformation to a log scale for the regression is usually recommended.

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12-02-2014 12:37 PM

Hi Reeza,

Yes..sometimes...but in this case no....

there is no outliers in errors, and they are normally distributed (p value of Shapiro-Wilk test is 0,873), there is some degree of autocorrelation (U from Durbin-Watson test = 1,92) and heteroscedasticity (p value of Breusch - Pagan test is 0,445) , but i'm using Newey-West standard errors to resolve this issues..

Tnx

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12-02-2014 02:49 PM

Hi,

You are concerned about the big numbers, which seem to be inconsistent with your analyses expectations. Looking at your plot. it is evident that there are two groups of values around the straight line one at the start and second at the end of the line. I would suggest do some segmentation before running the regression analysis. It may lead towards better estimates within each segment and as a result better predictions.

Solution

12-02-2014
03:58 PM

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12-02-2014 03:58 PM

The strait line provides a reasonable fit to your data. In most situations, a change of one pH unit is a major change. Just use as a unit what is useful for interpretation in your field. Don't forget that the center of the pH scale is around 7 for most people, thus the magnitude of the intercept (i.e. zero is very far away).

PG

PG

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12-02-2014 04:10 PM

Thank you PG,

That's the answer i wanted to hear.....((pH chagne by one (either in plus or minus) is not possible with this exp. design))..

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12-02-2014 06:11 PM

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12-02-2014 07:10 PM

First (lower) cluster was made by two groups. Relationship between a* and pH for only this two groups are strong linear and indentical to your marking on picture, but relationship between a* and pH for 3rd group only, is strong cubic...

Perhaps the relationship between those two variables will be different if there is more samples per group. However, those changes are caused by the salt penetration in fish muscle (by osmosis process) which leads to a protein denaturation - the fall of the pH value and decrease colour values (in red - green spectrum).

From my perspective and goal of analysis, i will describe relationship between those variables through entire salting process (2, 4 and 6 hours - which represent groups)....

However, i really appreciate your help..tnx

Tomislav