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I tried to use a linear model to explain a variable "age" with two variables "x1" and "x2".

I can clearly see a decreasing slope inside my scatterplot for age vs x1, or age vs x2, and the pvalue of each coefficient of my model is <0.001, but there is too much dispersion (R2 of my linear model is < 0.5).

I don't have much information, so i would like to add a "prior" information, the "exact distribution" of "age" inside a population, using the population censing of my country (which then does not depend on "x1" or "x2" ...). Hope this helps to narrow down the error. I'm not sure if I can do that, and if yes, how ?

I'm sure the linear model is a suitable model to explain the relationship between age and x1 and x2, but it cannot make precise predictions.

Knz
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  • Welcome to Cross Validated! I am confused about what you mean in your final sentence. “ I'm sure the linear model is a suitable model to explain the relationship between age and x1 and x2, but it cannot make precise predictions,” seems logically inconsistent. – Dave Sep 23 '22 at 13:24
  • Thanks ! :).

    It can't make an accurate prediction on the age variable, because x1 and x2 don't capture much of the observed variation, but age depends linearly on x1 or x2, the relation is well explained

     – Knz Sep 23 '22 at 13:36
  • Would it be fair to say that you are missing a key determinant of the outcome and will not be able to access that information? – Dave Sep 23 '22 at 13:40
  • A key determinant of the outcome ? – Knz Sep 23 '22 at 13:43
  • The distribution of age in your population will likely not be very useful. Any knowledge of how your x1 depends on age may be useful (this is what Bayesians mean by a "prior"). If there are nonlinearities in the response, you could try spline transforms, or loess, or some other kernel smoother. However, often there simply is a lot of residual variation, and we simply can't predict as well we we would like to. How to know that your machine learning problem is hopeless? – Stephan Kolassa Sep 23 '22 at 13:43
  • Thank You @StephanKolassa – Knz Sep 23 '22 at 13:49

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