Question about correlation and regression

[abollo]

Hi guys
My question may sound a bit dumb so please excuse me

In regression in data analysis isn't multiple r the coefficient of correlation?
And if so shouldn't the function CORREL yield the same answer if used on the same data sets

Because I tried comparing the number of the data analysis and correl and I got once a positive number in data analysis (0.75) and its equivalent negative number while using correl (-0.75).

Why is that?

Thanks alot

 

[abollo]

anyone?

 

[GooberTron]

Multiple R is generally used when you have more than 1 predictor variable. In the case you only have 1 predictor variable it should be equal to the square root of the RSQ() function, which should also give you the same result as CORREL(). I just tried it on some dummy data and it matched up.

 

[abollo]

Firstly thanks for the reply.

Can you try it with this data?

[TABLE="width: 221"]
<colgroup><col><col></colgroup><tbody>[TR]
[TD]Empolyment Age[/TD]
[TD]Salary[/TD]
[/TR]
[TR]
[TD]21[/TD]
[TD]200[/TD]
[/TR]
[TR]
[TD]18[/TD]
[TD]250[/TD]
[/TR]
[TR]
[TD]19[/TD]
[TD]500[/TD]
[/TR]
[TR]
[TD]25[/TD]
[TD]500[/TD]
[/TR]
[TR]
[TD]19[/TD]
[TD]750[/TD]
[/TR]
[TR]
[TD]18[/TD]
[TD]1000[/TD]
[/TR]
[TR]
[TD]18[/TD]
[TD]1000[/TD]
[/TR]
[TR]
[TD]26[/TD]
[TD]1000[/TD]
[/TR]
[TR]
[TD]17[/TD]
[TD]2000[/TD]
[/TR]
[TR]
[TD]18[/TD]
[TD]2000[/TD]
[/TR]
[TR]
[TD]24[/TD]
[TD]2500[/TD]
[/TR]
[TR]
[TD]25[/TD]
[TD]2500[/TD]
[/TR]
[TR]
[TD]19[/TD]
[TD]3500[/TD]
[/TR]
[TR]
[TD]20[/TD]
[TD]4000[/TD]
[/TR]
[TR]
[TD]17[/TD]
[TD]5000[/TD]
[/TR]
[TR]
[TD]18[/TD]
[TD]5000[/TD]
[/TR]
[TR]
[TD]20[/TD]
[TD]5000[/TD]
[/TR]
[TR]
[TD]17[/TD]
[TD]5000[/TD]
[/TR]
[TR]
[TD]17[/TD]
[TD]5000[/TD]
[/TR]
[TR]
[TD]19[/TD]
[TD]5000[/TD]
[/TR]
[TR]
[TD]21[/TD]
[TD]5000[/TD]
[/TR]
[TR]
[TD]25[/TD]
[TD]5000[/TD]
[/TR]
[TR]
[TD]25[/TD]
[TD]5000[/TD]
[/TR]
[TR]
[TD]17[/TD]
[TD]6000[/TD]
[/TR]
[TR]
[TD]21[/TD]
[TD]6000[/TD]
[/TR]
[TR]
[TD]19[/TD]
[TD]6000[/TD]
[/TR]
[TR]
[TD]17[/TD]
[TD]7000[/TD]
[/TR]
[TR]
[TD]21[/TD]
[TD]7000[/TD]
[/TR]
[TR]
[TD]17[/TD]
[TD]8000[/TD]
[/TR]
[TR]
[TD]19[/TD]
[TD]8000[/TD]
[/TR]
[TR]
[TD]29[/TD]
[TD]8000[/TD]
[/TR]
[TR]
[TD]17[/TD]
[TD]9000[/TD]
[/TR]
[TR]
[TD]18[/TD]
[TD]9000[/TD]
[/TR]
[TR]
[TD]19[/TD]
[TD]10000[/TD]
[/TR]
[TR]
[TD]19[/TD]
[TD]10000[/TD]
[/TR]
[TR]
[TD]25[/TD]
[TD]10000[/TD]
[/TR]
[TR]
[TD]20[/TD]
[TD]12000[/TD]
[/TR]
[TR]
[TD]20[/TD]
[TD]12000[/TD]
[/TR]
[TR]
[TD]20[/TD]
[TD]13000[/TD]
[/TR]
[TR]
[TD]25[/TD]
[TD]13000[/TD]
[/TR]
[TR]
[TD]17[/TD]
[TD]14000[/TD]
[/TR]
[TR]
[TD]19[/TD]
[TD]15000[/TD]
[/TR]
[TR]
[TD]24[/TD]
[TD]15000[/TD]
[/TR]
[TR]
[TD]19[/TD]
[TD]20000[/TD]
[/TR]
[TR]
[TD]22[/TD]
[TD]20000[/TD]
[/TR]
[TR]
[TD]19[/TD]
[TD]30000[/TD]
[/TR]
[TR]
[TD]18[/TD]
[TD]30000[/TD]
[/TR]
[TR]
[TD]24[/TD]
[TD]30000[/TD]
[/TR]
[TR]
[TD]18[/TD]
[TD]35000[/TD]
[/TR]
[TR]
[TD]18[/TD]
[TD]45000
[/TD]
[/TR]
</tbody>[/TABLE]


CORREL gives me -0.07498, while the square root of RSQ gives me 0.07498 and the regression analysis too. Judging from the values and from a scatter diagram I think the relationship is negative

 

[GooberTron]

Yes - but by definition a squared term like the algebraic calculation of RSQ() will only ever return a positive value - so there are two solutions to the square root of RSQ() - a positive and negative value i.e. +/- SQRT(RSQ). This is where CORREL (i.e. before squaring) is helpful in telling you whether your response generally increases or decreases as your predictor variable increases.
Also, multiple R is the positive square root of R^2 - so you will only see positive values for it.