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I have a table in which the multiple linear regression results is provided. If I have unstandardized coefficients and standard error for each independent variable, is it possible to calculate standardized coefficient (Beta) and coefficient of determination ($R^2$) from these data.

My friend provided $R^2=0.41$ for these data, but I doubt if the results are reliable. I brought the table in the following, would you please compute Beta and R-squared for me to compare with the original table?

enter image description here

the descriptive statistics is the following table:

enter image description here

user31315
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  • This question cannot be answered with the information given: the computation requires the standard deviations of the explanatory variables. Please consult threads associated with the [tag:standardization] tag, such as http://stats.stackexchange.com/questions/74622/converting-standardized-betas-back-to-original-variables, which shows how to compute the unstandardized coefficients from the betas (and, when carried out in reverse, essentially answers your question). – whuber Nov 15 '13 at 16:32
  • thanks a lot for the comment. I provided standard deviations of variables. then is it possible to estimate beta and r-squared from these data? – user31315 Nov 15 '13 at 17:01
  • Yes: use the method explained in the answer I referenced. – whuber Nov 15 '13 at 17:04
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    Among other places, see also a comment [here](http://stats.stackexchange.com/q/73103/3277), to convert b to beta. – ttnphns Nov 15 '13 at 17:07
  • @whuber and ttnphns: Thank you. sorry if I'm taking your time. I don't know anything about statistics and I could not understand the formula. would you please do the procedure for one variable to see how you substitute the values in the formula mentioned in the link you provided and calculate beta and R-squared ? for example for variable 'r' in the above table – user31315 Nov 15 '13 at 17:25
  • No knowledge of stats is needed because this is just arithmetic: as the other answer shows, you simply divide the standardized coefficients by the standard deviations to get the coefficients, whence to go the other way you just multiply the coefficients by the standard deviations to get the standardized coefficients. You can also standardize the outcome variable as shown in that answer. – whuber Nov 15 '13 at 17:31
  • For r, its std. coefficient is then: -.185 * 1.44875 / (standard deviation of the dependent variable). Since you didn't the SD of the dependent variable here, I can't give you the answer. – Penguin_Knight Nov 15 '13 at 17:43
  • @ whuber, @ Penguin_Knight: Many Many thanks for your helpful answers. really great help. Wish you the bests :) – user31315 Nov 15 '13 at 17:52
  • by the way, I forgot to ask about R-squared. how should I calculate it? – user31315 Nov 15 '13 at 18:49
  • Read it off the table. – whuber Nov 15 '13 at 19:49
  • yeah, I mean if I have not had it before, and want to calculate it from coefficients, is there any way for it? – user31315 Nov 15 '13 at 19:53

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