Achieve Linearity

Printable View

• Dec 1st 2009, 06:52 PM
IDontunderstand
Achieve Linearity
I have a data set that is not linear. I took the log of the dependent and independet variables which made the data linear. I get an equation of

ln y(hat)=-6.804+1.466 lnx

I know to get rid of the Ln on y(hat) side we take e

y(hat)= e^(-6.804+ ln x^ (1.499))

My notes tell me that I can say e^(-6.084) * x^(1.499)=y(hat)

What happened to the ln
• Dec 2nd 2009, 12:24 AM
CaptainBlack
Quote:

Originally Posted by IDontunderstand
I have a data set that is not linear. I took the log of the dependent and independet variables which made the data linear. I get an equation of

ln y(hat)=-6.804+1.466 lnx

I know to get rid of the Ln on y(hat) side we take e

y(hat)= e^(-6.804+ ln x^ (1.499))

My notes tell me that I can say e^(-6.084) * x^(1.499)=y(hat)

What happened to the ln

If:

$\ln (\hat{y})=-6.804+1.466 \ln(x)$

Then:

$
\hat{y}= e^{-6.804+1.466 \ln(x) } = e^{-6.804}e^{1.466 \ln(x) } = e^{-6.804}e^{\ln(x^{1.466}) }=e^{-6.804}\; x^{1.466}
$

CB