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PostPosted: Fri, 4 May 2012 20:17:08 UTC 
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Can one say that Multiple Regression could accomplish ANOVA?

I am thinking out loud here, so bear with me.

As I understand ANOVA, we are searching to see if there is a difference between groups.
Using Dummy Variables, could we not just perform Multiple Regression?

Or, can someone give me an example where ANOVA completes a task that Multiple Regression cannot.


I have been struggling with this since I began my Statistics studies.
I like ANOVA for its simplicity, but the more I learn, the more I learn that it can get complex.
And, each time I see an example, I think of it in terms of Multiple Regression.
Am I missing something? Any assistance is appreciated.


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PostPosted: Sat, 5 May 2012 06:08:21 UTC 
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Mr. Mathturo wrote:
Can one say that Multiple Regression could accomplish ANOVA?

I am thinking out loud here, so bear with me.

As I understand ANOVA, we are searching to see if there is a difference between groups.
Using Dummy Variables, could we not just perform Multiple Regression?

Or, can someone give me an example where ANOVA completes a task that Multiple Regression cannot.


I have been struggling with this since I began my Statistics studies.
I like ANOVA for its simplicity, but the more I learn, the more I learn that it can get complex.
And, each time I see an example, I think of it in terms of Multiple Regression.
Am I missing something? Any assistance is appreciated.


The difference between regression vs ANOVA is whether you have the ability to control precisely the independent variable(s). In ANOVA you have the ability to directly manipulate the factors and measure the result and we are trying to determine how much of the variations we can account for by manipulating the independent variables, whereas in regression analysis you can't control the independent variables and thus have to simply measure the naturally occuring independent variables to see if it helps us to predict the dependent variable.

So yes, you could use regression if you introduce dummy, but you lost the model intention if you do so.

_________________
\begin{aligned}
Spin(1)&=O(1)=\mathbb{Z}/2&\quad&\text{and}\\
Spin(2)&=U(1)=SO(2)&&\text{are obvious}\\
Spin(3)&=Sp(1)=SU(2)&&\text{by }q\mapsto(\mathop{\mathrm{Im}}\mathbb{H}\ni p\mapsto qp\bar{q})\\
Spin(4)&=Sp(1)\times Sp(1)&&\text{by }(q_1,q_2)\mapsto(\mathbb{H}\ni p\mapsto q_1p\bar{q_2})\\
Spin(5)&=Sp(2)&&\text{by }\mathbb{HP}^1\cong S^4_{round}\hookrightarrow\mathbb{R}^5\\
Spin(6)&=SU(4)&&\text{by the irrep }\Lambda_+\mathbb{C}^4
\end{aligned}


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