Table below presents the data resulting from an investigation into the effect of two variables, reaction temperature $($x$1),$ and reactant concentration $($x$2),$ on the percentage conversion of a chemical process $($y$).$

Create a quadratic polynomial approximation for dependency of the percentage conversion of a chemical process $($y$)$ on the two variables: reaction temperature $($x$1)$ and reactant concentration $($x$2).$

a$)$ Use the Sum of squares of errors as an objective

b$)$ Use maximum absolute error as an objective

c$)$ Try to fit some other approximation.

For example:

$-$ a higher order polynomial

$-$ a quadratic polynomial plus something else: exponent, power, log$,$ etc.

$-$ etc.

Which approximation you prefer and why?

Demonstrate using "Actual vs$.$ Predicted" plots and values of Root Mean Squared Error $($RMSE$),$ Avergae absolute error, Maximum Absolute error.

Table: