Simulate a "multiple" regression with two predictors problem by yourself, with sufficient sample size, e$.$g$.,50000$ samples.

$y={}_0+{}_1{x}_1+{}_2{x}_2+lon,lonN(0,{}^2).$

a$.(5\%)$ Use the regression package in your preferable environment $(R$ or Python$)$ to analyze the problem and review the results.

b$.(15\%)$ From the perspective of "machine learning," code the gradient descent method to optimize $($minimize$)$ the error function and get the coefficients. Do you get the same results as those in $($a$)?$ Demonstrate the evolution of the iterative errors and the searching path in the domain of the error function.

${?}^{**}$ Make any necessary assumptions by yourself if not mentioned above.