Use of R^2 adjusted in Simple Linear Regression-Excel?

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Discussion Overview

The discussion revolves around the use and meaning of adjusted R² in the context of simple linear regression as implemented in Excel. Participants explore the implications of this metric and its relevance when only one variable is used in the regression analysis.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about the meaning of adjusted R² in simple linear regression and questions what the adjustment entails.
  • Another participant suggests that the question is more about the interpretation of adjusted R² rather than its specific implementation in Excel.
  • Some participants argue that adjusted R² may not hold significant meaning in simple linear regression since there is no adjustment made when only one variable is included.
  • There is a concern raised about the potential misuse of statistical measures, likening it to operating complex machinery without proper qualifications.
  • One participant reiterates that adjusted R² is typically used to avoid distortions when additional variables are included, questioning how this applies when only one variable is present.

Areas of Agreement / Disagreement

Participants express differing views on the relevance and interpretation of adjusted R² in simple linear regression. Some believe it is not meaningful in this context, while others acknowledge its standard inclusion in outputs without fully agreeing on its implications.

Contextual Notes

There is uncertainty regarding the application of adjusted R² when only one variable is used, and participants highlight the lack of adjustment in this scenario.

WWGD
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Hi All,
I am kind of confused at the fact that Excel uses the measurement of adjusted ## R^2 ## for simple
linear regressions ; please see below. What does that even mean, what is the adjustment for?
upload_2017-2-23_18-57-9.png
 
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Did you consult the help file ? Anything there that specifically needs extra explanation ?
 
I think WWGD question is more aimed at what does an adjusted R squared value mean in terms of a simple linear regression as opposed to what it means just in excel. The simple answer is that it means nothing. It's probably just part of the standard output but it should more or less be aligned with the regular r squared value since there isn't an adjustment being made per say. (i.e. as is the case in this example).
 
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I sure hope you are right. I resent people taxiing with 747s when they don't even have a driver's license. And even then there's a risk they inadvertently take off.
 
BvU said:
Did you consult the help file ? Anything there that specifically needs extra explanation ?
Yes, essentially what Marne said: adjusted R-squared, AFAIK, is used in OLS to avoid distortions when additional variables are included. How does this make sense when we only use one variable?
 
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MarneMath said:
I think WWGD question is more aimed at what does an adjusted R squared value mean in terms of a simple linear regression as opposed to what it means just in excel. The simple answer is that it means nothing. It's probably just part of the standard output but it should more or less be aligned with the regular r squared value since there isn't an adjustment being made per say. (i.e. as is the case in this example).
Precisely. The adjustment is done for additional variables that are included, AFAIK.
 

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