I have some training set data variables $x_1$, $x_2$, $x_3$, $x_4$, and $x_5$ and a response variable $y$.
But these are time series data. So the for the same set of values of $x_1$, $x_2$, $x_3$, $x_4$, and $x_5$ the response variable $y$ may be different in different observations. Can anyone please suggest me how to model my linear regression in this case? I am learning newly statistics. Please explain in the simplest way possible.
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Best Answer
If your aim is to "detrend" the data (i.e., remove the "time dependent" component from your estimates), you can estimate the model as
$Y = \alpha + \beta t + \gamma_i X_i + \epsilon$
Where the $\beta t$ term captures your linear time variance and the $\gamma_i$ terms capture the marginal effect of your $X_i$s, assuming all your other modelling assumptions hold.
The time component in your data is referred to as "non-stationarity" and there is a whole literature on dealing with this sort of time-series analysis. The above is perhaps the simplest model you could suggest, however embodied in it is a huge set of assumptions about the state of your data generating process.