# Multiple Linear regression: inverse the y value

I have a dataset of 3500 samples where delay (dependent variable) depends on multiple system variables,such as cpu, memory, etc.

I can use a multiple regression model and predict the delay against a baseline (one system to be used as a baseline), or speedup, therefore instead of dealing with:

Delay values: 1000, 1500, 2000, 3000, ...

I deal with (for example, 3000 as the baseline):

Speedup ratios: 3, 2, 3/2, 1, ...

I understand that I have changed y = ax1 + bx2 + .. +c to 1/y = ax1 + bx2 + .. + c

So, the results of my regression model on values are:

R2 Score:  0.76
RMSE:  246.82
MAE:  173.31
Range of values is 0-3000, hence Normalised RMSE (NRMSE): 246.82/3000= 0.082


And the result of my regression model on ratios are:

R2 Score:  0.96
RMSE:  70.30
MAE:  43.86
Range of ratios is 0-4000, hence Normalised RMSE (NRMSE): 70.30/4000 = 0.017


Question: The use of a baseline was quite specific to my problem (as speedup made sense). And now I am wondering if such a conversion (inversing the outcome variable) would work for any other regression examples? Is this even common? or in other words, how would I know if conversions like that would work for a regression problem (is it called reverse linear)? In general, are there any clues I should be looking for?

• Re specification of a model(linear regression in your case) is common and depends on the problem your are trying to solve. Be aware that when changing the model, model quality measurements(R2, MAE, etc..) meaning changes too.(MAE 43.86 of the inverse model might be high regarding your needed accuracy). – yoav_aaa Jul 29 at 14:18
• @yoav_aaa, thanks. Yes, different MAEs make sense as I am inversing the output and scaling it too. Are there any tests to be done on the data set to know if such a conversion is useful? I could not find any useful information on how to know such a transformation would work – towi_parallelism Jul 29 at 14:31