Hi,
I have a situation where I need to find the value of independent variables for a given value of a dependent variable (just opposite of what regression does). This could be easily achieved for Linear Regression models as their inverse is possible, however if the model is non-linear in nature like Polynomial Regression or ARIMA then is there a way to find this value.
Also kindly suggest if there are other possible suggestions other than finding the inverse of the function.
My use case is like I have a time series with CPU utilization as the dependent variable. Creating a forecasting model I could predict the CPU utilization at any given time in future. However in second use case I need to find the data/time on timeseries when CPU utilization could have a specific value.
Thanks
I think the best solution is to plot the data, i.e the forecast values vs date/time. The value of independent variable can then be obtained by drawing projection from the specific value of CPU utilization on x-axis.
@Thomas Brey : I already tried this approach. However when we reverse the nature of parameters the nature of fitting curve also changes. Like if I am doing Linear least square regression, fitting a polynomial of order 2, taking 'x' as independent and 'y' and dependent, then the plotted curve shows that at least we could have some y=y1 in future although we don't know the 'x1' for that 'y1' (that's what we are trying to find). While if we reverse the order and make 'y' independent and 'x' dependent then the relationship completely changes and sometimes the graph shows that instead of having 'y1' in future we are getting 'y1' in past :(
I agree with Farah, plotting (the historical data) will be helpful.
While your problem may be mathematically challenging. I doubt its practical sense.
Why?
First, you can only plot and make a model out of historical data. Beyond that, you need first the value of the independent variable to estimate or predict the value of the dependent variable.
Therefore you cannot have predicted values of the dependent variable to calculate the value of the independent variable because getting the predicted value of the dependent variable REQUIRES first the value of the dependent variable.
This is call a calibration problem in statistics. Look for this in nonlinear regression
@Basilio: This is exactly what I am looking for. Many thanks for sharing.
If your model is of second degree polynomial, then we could find an analytical relation between x and y. For an example look here:
https://www.researchgate.net/post/Can_a_bivariate_random_dataset_be_nonlinear_and_polysemic_at_the_same_time/1
where the x-y equation was found easily, see my attachment there.
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