# What kind of model is this and how do you estimate its parameters?

For the following model:

$$T = A_0 + A_1M+ A_2M^2 + A_3\ln(P) + A_4\ln(P)^2+A_5M\ln(P)$$

where:

$T$ = Dependent variable

$P$ = Independent variable

$M$ = Independent variable

$A_0 \dots A_5$ = Coefficients of the regression.

I would like to know which class of regression model this equation corresponds to, when you use this kind of model, and how you find the parameters $A_0 \dots A_n$.

• It's a polynomial regression model of degree two (or sometimes, a 'quadratic model') in two predictors, ($M$ and $\ln P$). You estimate the coefficients the same way as for any other multiple regression. – Glen_b -Reinstate Monica Jun 10 '13 at 13:27
• hi Glen_b: by chance would you know why there is used the "Ln()"? – user26695 Jun 10 '13 at 17:46
• Presumably because whoever built the model felt that whatever T was would be more nearly linearly related to lnP than to P; without context and subject knowledge, it's impossible for me to say much. – Glen_b -Reinstate Monica Jun 11 '13 at 0:55