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tslm(Life_expectancy ~ Age + Gender + Race + trend, data=ts_df) 

Can I do something like this? I actually tried using this as a model and I got a different outcome but the p-value of trend variable was insignificant. Does that mean that there is no trend in my data?

I did the vif test. vif result

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From my experience, trend variable is quite commonly used in time series regression. Especially in Demand Forecasting. I therefore can't see any problem using trend.

Having an insignificant p-value for the trend coefficient does not imply your dataset doesn't have any trend. There could be other reasons for that, the most immediate I can think of - a large sd for the trend coefficient.

To me, it might be that the trend and Age variables are correlated with each other, causing the trend p-value to shrink. I'd suggest measuring the VIF and correlation for your variables, focusing on examining the Age and trend relationship.

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  • $\begingroup$ Thanks for the explanation. I did the vif test and it shows that the variables are highly correlated. So, what can I conclude from here? I am a bit confused here. My goal is actually to find the variables that have the most influence on life expectancy by using tslm. $\endgroup$ Jun 29, 2023 at 18:46
  • $\begingroup$ I'd suggest try to collect more data. It seems to me that your dataset is measured at a single point in time. If you can't, try feature selection. Remove Age\trend and see if it helps. Other approaches: instead of linear trend try using logarithmic, quadratic etc. trend. Those are the immediate solutions. $\endgroup$
    – Alex Teush
    Jun 29, 2023 at 19:20
  • $\begingroup$ Thanks for the explanation. Actually my objective is to fit tslm and lm model to my data set and select which model is suitable for time series data. But, I found out that both the models are the same unless I add variables trend for tslm() model. That's why I was asking whether I can include trend variable in my tslm model. $\endgroup$ Jun 30, 2023 at 5:47

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