why isnt multicollinearity a factor in exponential regressions?
Speculating … Exponential form implies that as X increases, Y increases at a faster rate … so maybe that mitigates multicollinearity’s effects? I have no clue. Please update the thread if you find out.
Exponential regressions with just one independent variable perhaps?
It definitely has an effect in multiple regressions
A variable is regressed against three other variables, x, y, and z. Which of the following would NOT be an indication of multicollinearity? X is closely related to: A) 3y + 2z. B) y^2. C) 3. Your answer: B was correct! If x is related to y^2, the relationship between x and y is not linear, so multicollinearity does not exist. If x is equal to a constant (3), it will be correlated with the intercept term.
well according to schweser pg 203, by definition it is linear, but i want to know why it doesnt affect exponential regressions.
Because if x=y^2 it is a transformed variable and no longer redundant (recall: to correct for multicollinearity you drop the most highly correlated variable), the reason you don’t want variables that are linear combos of one another in a regression is because they basically explain what is already explained by the other variable/s of which they are a linear combination. It is perfectly normal/correct to have a regression such that you have y=a+bx+cx^2, x^2 is transformed and may have a different relationship with y then just x. This sort of transformation is typical/common, let me demonstrate with an example: Suppose we know our data follow a perfect sinusoidal-type curve (on some interval where it goes through one full cycle), we also know from calc the the highest exponent in an equation indicates the number of different slopes (ex. if highest exponent is 3, the graph will have a segment with a positive slope followed by a segment with a negative slope, and then a positive slope again; or vice versa) when we graph that curve. This graph can then be described (if we take any given segment) as y=a+x^3 or depending on other properties it may be better described by y=a+bx+bx^2+cx^3, the point being that the highest exponent remains three and we still have a graph which changes slope twice and has three distinctly sloped segments. Hope that helps.