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This is result from Generalized Additive Model. I am trying to look at the relationship between the number of deaths(dependent variable) and PM2.5 (independent variable) with lag effect. However, I do not know how to interpret it. Is the p-value is important in this Model? What is important and how the result should be ? Please explain me if someone who is good at GAM.

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It looks as if none of the terms in your model are significant except for the smoothing terms for time and month suggesting a nonlinear relationship over time (non-linear trend) coupled with a seasonal signal of some kind. You're R-Squared is pretty low at 18%.

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