Best ML technique to suggest predictor variables
STEP 1

When you do Regression on this dataset, what you obtain is: 

$\hspace{60mm}f(x_1,x_2,x_3,x_4) = ERI$

where your $x_1,x_2,x_3,x_4, ERI$ are O2 level, Cylinder Pressure, Fuel Flow,, Engine Temp, and Engine Running Indexrespecetively.
In case of Multiple Regression, you will get 1 coefficient per feature (total 4 in coef_, {$w_1,w_2,w_3,w_4$}) and one intercept_ ($w_0$) term for the intercept. Your equation would then come to look like:

$\hspace{40mm}ERI = w_1 x_1 + w_2 x_2 +w_3 x_3 +w_4 x_4 +w_0$, 

where $w_0$ - $w_4$ are fixed values. Your objective then is to find the best $x_1$ - $x_4$ which maximize $ERI$. 

STEP 2

The above is better expressed by the optimization problem:

$\max_{(x_1,x_2,x_3,x_4)} w_1 x_1 + w_2 x_2 +w_3 x_3 +w_4 x_4 +w_0$
with constraints that $x_1,x_2,x_3,x_4 \geq 0$ 

I added those constraints by default as all those variables would be positive only. You could have upper limits on each of them as well. It is important to add these constraints because you don't want any of your value to reach $\infty$ or even some unrealistic values like Engine Temp = $10^6$.

The above function is the objective function which you want to maximize, OR you can minimize the negative of the same. Both of them are equivalent. Thus your objective becomes:

$\min_{(x_1,x_2,x_3,x_4)} -(w_1 x_1 + w_2 x_2 +w_3 x_3 +w_4 x_4 +w_0)$
with constraints that $x_1,x_2,x_3,x_4 \geq 0$

From here, you can use Scipy's Minimization function with the Objective function we just came up with.