Below $is$ the question from $my$ statistics class and $my$ answer about multiple regression. Are $my$ IVs $in$ the correct order? how good $is$ the $MR$ equation? The professor used parenthesis $(withe).$ Should I include the coefficients $or$ not? Class $1$ Question:

Choose $aMR$ model that you would like $to$ assess and indicate how you would enhance the traditional $MRto$ include expanded error. Your answer can $be$ simple with the traditional $MR$ model and then the enhanced $MR$ model with expanded error. Indicate how the dependent variable and independent variables relationships might change $if$ the expanded errors are allowed $to$ correlate. The traditional formula $is$: $fy=x1+x2+x3+x4+x5+e.$ When $we$ allow for expanded error $we$ have $fy=x1(withe)+x2(withe)+x3(withe)+x4(withe)+x5(withe)$

Please include the one dependent variable and a minimum $of$ three and $no$ more than five independent variables $in$ your answer.

Class $1$ Answer:

A Model $to$ assess $an$ Operations Research System Analyst $(ORSA)$ Productivity.

The dependent variable $is$ productivity score $(y).$

The independent variables are:

$*x1=$ years $of$ experience

$*x2=$ training $(hours$ per year$)$

$*x3=$ number $of$ completed projects $(per$ year$)$

$*x4=$ position $(lead,$ supporting role$)$

When expanded errors are allowed, the model becomes:

$fy=a1x1+a2x2+a3x3+a4x4+e1(x1)+e2(x2)+e3(x3)+e4(x4)$

where $a1$ through $a4$ are the coefficients and $e1(x1)$ through $e4(x4)$ are the expanded error terms.

The coefficients $a1$through $a5$ will capture the main effects $of$ the independent variables, while the expanded error terms account for correlated errors.

$Ifwe$ allow the errors $(e)to$ correlate the greatest correlated errors might occur between:

$1.e1(yearsof$ experience$)$ and $e2(hoursof$ training$)$: $If$ more experienced ORSAs are receiving less training $(e1$ and $e3$ are negatively correlated$),$ this might indicate that more experienced ORSAs benefit less from training $(e.g.,$ training may have less impact $on$ more experienced ORSAs, potentially reducing productivity$).$

$2.e4(position)$ and $e2(hoursof$ training$)$: Those $in$ lead positions might receive $or$ require different training levels compared $to$ those $in$ supporting roles, leading $to$ a potential correlation here $as$ well. Misaligned training for leads might reduce their productivity.

$3.e1(yearsof$ experience$)$ and $e3(numberof$ completed projects$)$: More experienced ORSAs might complete more projects, leading $to$ a positive correlation between these errors, suggesting that experience contributes directly $to$ project completion, which $in$ turn affects productivity.