Classic Linear Regression Model Assumptions

[Galli]

“The relationship between the dependent variable, Y, and the independent variable, X is linear in the parameters b0 and b1. This requirement means that b0 and b1 are raised to the first power only and that neither b0 nor b1 is multiplied or divided by another regression parameter. The requirement does not exclude X from being raised to a power other than 1.”

This seems like a silly “assumption” of a linear regression model. Feels to me it’s saying something as obvious as, to be a German Shepard, the specimen must be a canine.

Am I missing anything else critical with this first assumption?

 

[S2000magician]

I’d say, no.

 

[RiskMgr]

They’re trying to get you to think about using transformations for your variables.
In OLS linear regression, we often have to model relationships that are non-linear. The assumption that the X & Y are linear in the parameters is to make sure your parameters (i.e. betas) are indeed linear. The only way this can happen in many cases is to force them into compliance by transforming your independent (and sometimes dependent) variables.
If you have data that has a quadratic or logarithmic line of best fit and try to use linear regression, you won’t properly identify the relationship that exists in the population. The fix to that is simply respecifying your model to include transformed variables (years of education on income, for instance, begs for a log transformation, or anything else that exhibits diminishing returns).
It’s pretty clear that the CFAI quant materials weren’t written by econometricians, but that’s probably not the point here. The only way I could see testing this would be if they gave you a scatter plot with a line of best fit and asked which OLS assumptions were violated. Or perhaps one that asked you which violation of OLS assumptions would be corrected by transforming a variable. Alternatively, a trap question question could be asked where you are given a model and regression output where multicollinearity existed but they try to trick you into selecting “not linear in the parameters” because the model had a squared or logged variable. Or maybe one where the betas were squared, which WOULD be a violation of this assumption of OLS.
Just my interpretation at what they are getting at. Good luck to you in your studies!