Question
Asked 10th Apr, 2015

Can anyone explain what is the difference between B and β, in multiple regression?

Hi, i am using multiple regression for one of my papers and i came across two types of B; B  and β, for which i don't understand the difference. Looking for answers in books and internet made it worse. Some say that β is the power, or similar to the alpha level, and some say that it is the beta weight. But if β is the beta weight, then what does the B stands for?
Thanks in advance

Most recent answer

18th Jan, 2022
Aishath Naila
The Maldives National University
B is an unstandardized coefficient which means original units besides the slope and tell if the independent variable is a significant predictor of the dependent variable. Beta is a standardised coefficient between -1 to +1 in range and show the strength of the prediction

All Answers (20)

10th Apr, 2015
Manfred Hammerl
Karl-Franzens-Universität Graz
"then what does the B stands for"
b always is for the unstandardised regression coefficient (while beta is the standardised one).
1 Recommendation
10th Apr, 2015
Kalliopi Tzani
University of Huddersfield
Hi Manfred, thanks for your answer. So when comparing for which independent variable contributes mostly for a change in the dependent variable, the beta is more appropriate to look at and report? 
11th Apr, 2015
Kalliopi Tzani
University of Huddersfield
Charles thank you, i got it now. Thank you for being analytic and providing the examples.
7 Recommendations
11th Apr, 2015
Emilio Pariente-Rodrigo
Servicio Cántabro de Salud
Hi, Calli.
The question you pose moves me to share a doubt.
Sometime I came across this additional analysis about beta-coefficients, based on their comparability: The sum of all betas provides a total amount and you can calculate the weighted value (percentage) of each beta. That percentage therefore may represent the relative importance of each factor within the equation of the regression model.
I would like to hear arguments about this procedure.
Regards.
1 Recommendation
11th Apr, 2015
Jochen Wilhelm
Justus-Liebig-Universität Gießen
Charles and Manfred,
I don't see that this is a general rule. Some statistics software name it this way, others name it differently, and in books it is different again.
To understand what a letter or symbol means one has to refer the context (software manual, book, paper).
I agree that it is confusing that not always the same symbol is used for the same thing. But there is no natural law dictating that this has to be like that. We always must take care of the context. Referring to "general rules" (like "b always is for the unstandardised regression coefficient" - to cite Manfred) is generally not helpful...
I think a better answer is: To understand what a letter or symbol means you must read what the author said it is supposed mean in their text. When you consult different sources from differen authors, the very same letter/symbol may have a different meaning, so this is not helpful. If you wonder, for instance, what "B" means in an SPSS output, then you should refer the SPSS manual. If you wonder what "b" means in the book "Modern statistics of Life Sciences" then you should find the answer within this book. If people talk about "Paul" you will have to ask these people what person they are talking about. There is no general rule what kind of person has to have the name "Paul".
2 Recommendations
13th Apr, 2015
Sangita C. Patil (Birajdar)
MAEER’s Arts, Commerce and Science College
According to my knowledge if you are using the regression model,  β   is generally used for denoting population regression coefficient and B or b is used for denoting realisation (value of) regression coefficient in sample.
3 Recommendations
15th Apr, 2015
Pierre Souren
Radboud University
@Sangita,
That is another meaning of beta. Often greek symbols are used to refer to population values (mean (sample) vs mu (population) etc). But not in the case of regression outcomes.
Beta (often) is the standardized regression coefficient; as written before. And always keep an eye on the context; there is no general rule for the interpretation of symbols, as also has been written before.
About comparison of beta's I like to add:
this is only valid within a regression, not between regressions.
Example:
consider 3 regression analyses:
1. x1 and z1 are predictors (x1.y1; z1.y1) in a regression for y1
2. x1 and m are predictors (x1.w; m.w) in a regression for w
3. x1 and z1 and v are predictors (x1.y2; z1.y2; v.y2) in a regression for y2(=y1)
You can compare the betas of x1.y1; z1.y1
You can compare the betas of x1.w; m.w
You can compare the betas of x1.y2; z1.y2; v.y2
But you cannot compare the betas of: x1.y1; x1.w; x1.y2 even if it concerns the same predictor: x1. (and in case of x1.y2 also the same dependent variable)
Als, you cannot compare the betas of x1.y1; m.w.
and so on.
If you want to compare regression coefficients over regressions, use f-square; the effect size of the regressioncoefficient.
Greetings, Pierre
2 Recommendations
2nd Apr, 2017
Mohammed Zannah
Mai Idris Alooma Polytechnic Geidam Yobe Nigeria
A standardized beta coefficient compares the strength of the effect of each individual independent variable to the dependent variable. The higher the absolute value of the beta coefficient, the stronger the effect. For example, a beta of -.9 has a stronger effect than a beta of +.8. Standardized beta coefficients have standard deviations as their units. This means the variables can be easily compared to each other. In other words, standardized beta coefficients are the coefficients that you would get if the variables in the regression were all converted to z-scores before running the analysis.
5 Recommendations
15th Jul, 2017
Ujjal Deka Baruah
Cotton University
1. B is the rate of change per unit time
2. Beta is the correlation coefficient range from 0-1, higher the value of beta stronger the association between variables.
5 Recommendations
15th Jul, 2017
Mohammed Zannah
Mai Idris Alooma Polytechnic Geidam Yobe Nigeria
standardise and unstandardise coeffiecient.
1 Recommendation
8th Nov, 2018
Yiqun Lin
The University of Calgary
I believe beta is a parameter and b is a statistic.
Parameters refer to population level and statistic is a sample level. Same idea as population mean (mu) and sample mean (x-bar).
1 Recommendation
11th May, 2020
Md. Moniruzzaman
Putra Business School
Excellent clarification from Charles!
Thanks to him.
12th Dec, 2020
Sana Waris
Riphah International University
Really helpful..
Great work
Thanks!
23rd Feb, 2021
Oluwaseun Adegbilero-Iwari
Afe Babalola University
Contributions were helpful.
18th Jun, 2021
Mirosław Grzesik
Insitute of Chemical Enginering Polish Academy of Sciences
I do not think that such a question can be answered at all without providing additional information. One can only guess what the questioner means.
6th Oct, 2021
Nishikant Singh
ICMR- National Institute of Cancer Prevention and Research

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