how do you know weather a statistical model with a regression line is linear or non linear?

Answer 1

When statisticians talk about a linear model they mean linear in the parameters (not in the x's). For example

y = a + bx both linear in the paramaters and in the x's

y = a + bx + c*sin(x) is linear in the paramters but not in the x's. This is still a linear model

y = a*x^b is considered a transformable linear model since if I take the log of both sides I get log(y) = log(a) + b*log(x) and in terms of log(y), this is a linear in the parameters (even though there is a log(a) term that doesn't matter since I can write it as A + b*log(x) which is linear in terms of A and b where A =log(a)).

y = a + (d - a)/(1 + (x/c)^b) is not linear in the parameters nor can it be transformed into a linear model. This is an example of a nonlinear model.

Math (and Stats) Rule!

Answer 2

If the regression line can be manipulated to arrive at y = a + bx it is linear in x. The regression FORM is linear even with curves such as nth degree polynomials, y = ab^x, and y = ae^bx. (In other words, you still use linear regression to arrive at your constants) I've heard of non-linear regressions, but shudder at the thought of deriving or trying to apply one.

Answer 3

If there's a one-to-one correspondence in the climate in 2 contraptions of archives, the variety is linear, else it rather is non-linear, a quadratic being considered one of a limiteless style of non-linear fashions. ...