Proportion of total variation is accounted for by explained variation

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Discussion Overview

The discussion revolves around calculating the proportion of total variation accounted for by explained variation in a statistical context, specifically relating to the relationship between "emotional stability" and college performance. Participants explore the necessary information and methods for this calculation, including references to correlation coefficients and ANOVA.

Discussion Character

  • Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant questions whether the provided data is sufficient to calculate the proportion of total variation, noting the need for actual values.
  • Another participant suggests that partitioning total variance can be done using ANOVA methods, indicating that there is only one predictor variable in this case.
  • A different participant mentions that the Wikipedia article on "explained variation" states it may be considered as the square root of the correlation coefficient, suggesting a potential pathway to find the explained variation.
  • One participant asserts that 100r^2 represents the percentage of total variance explained by linear regression.

Areas of Agreement / Disagreement

Participants express differing views on the sufficiency of the provided information for calculating explained variation, with some advocating for the use of ANOVA and others questioning its applicability without group information. There is no consensus on the best approach to take with the given data.

Contextual Notes

Limitations include the lack of actual values needed for calculations and the uncertainty regarding the applicability of ANOVA without group data.

scolty
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Hi, I've come across a question in a stats book which asks the following:

Q: A study was undertaken to find the relationship between "emotional stability" and performance in college. The following results were obtained:
Emotional stability, Mean = 49, Standard Dev = 12
College Average, Mean = 1.35, Standard Dev = 0.5
pearson r = 0.5
n = 60

What proportion of total variation is accounted for by explained variation?

As far as i was aware, i need to know the actual values in order to be able to calculate this (ie summation of (Yprime - Ymean)^2) but the above info is the only supplied information. Have i missed something? If so id appreciate it if someone could point it out. Thanks.
 
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scolty said:
Hi, I've come across a question in a stats book which asks the following:

Q: A study was undertaken to find the relationship between "emotional stability" and performance in college. The following results were obtained:
Emotional stability, Mean = 49, Standard Dev = 12
College Average, Mean = 1.35, Standard Dev = 0.5
pearson r = 0.5
n = 60

What proportion of total variation is accounted for by explained variation?

As far as i was aware, i need to know the actual values in order to be able to calculate this (ie summation of (Yprime - Ymean)^2) but the above info is the only supplied information. Have i missed something? If so id appreciate it if someone could point it out. Thanks.

Partitioning total variance among different sources is accomplished by Analysis of Variance (ANOVA) methods. In your case, there is only one named predictor variable, so you would partition the total variance between "emotional stability" and "other". ANOVA also compares variance within groups with variance between groups.

http://www.sjsu.edu/faculty/gerstman/StatPrimer/anova-a.pdf
 
Last edited:
scolty said:
As far as i was aware, i need to know the actual values in order to be able to calculate this (ie summation of (Yprime - Ymean)^2) but the above info is the only supplied information. Have i missed something? If so id appreciate it if someone could point it out. Thanks.

The Wikipedia currently has an interesting article on "explained variation" and mentions that some people consider it to be the square roof of the correlation coefficient. You could find the correlation coefficients since you know r.

I don't think you'll make any progress trying to use ANOVA calculations on the given information since you don't know have any information about the subjects being divided into groups.
 
100r^2 is the %-age of total variance explained by linear regression.
 

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