To examine whether there is a pay discrimination between white and non$-$white employees, the compensation manager in your company has collected a data on annual salary, race $($white $=0,$ non$-$white $=1),$ work hours per day, rank $($non$-$managerial rank $=0,$ managerial rank $=1),$ and performance $(5$ point scale$).$ Below are the results of the linear regression analyses that the compensation manager has conducted.

Equations Regression Equation

P$-$value of the

coefficient for Non$-$White

Equation $1$ Annual pay $=-12,000*$ Non$-$White $+48,0000\mathrm{.}003$

Equation $2$ Annual pay $=-800*$ Non$-$White $+1,800*$ Work hours $+31,0000\mathrm{.}783$

Equation $3$

Annual pay $=-11,700*$ Non$-$White $+730*$ Managerial Rank $+312*$ Performance $+45,600$

$0\mathrm{.}005$

Equation $4$

Annual pay $=-501*$ Non$-$White $+1,920*$ Work hours $+560*$ Managerial Rank $+287*$ Performance $+28,300$

$0\mathrm{.}827$

From the results above, answer the following questions.

$-$ Is there a raw difference in pay between white and non$-$white employees? $(1)$

$-$ If there is a raw difference in pay between white and non$-$white employees, what seems to be the reason$($s$)$ for this difference? $(2)$

Group of answer choices

$(1)$ No$,(2)$ No raw difference

$(1)$ Yes, $(2)$ Rank

$(1)$ Yes, $(2)$ Both performance and rank

$(1)$ Yes, $(2)$ Work hours