Profitability remains a challenge for banks and thrifts with less than $$2$ billion of assets. The business problem facing a bank analyst relates to the factors that affect return on assets $($ROA$),$ an indicator of how profitable a company is relative to its total assets. Data collected from a sample of $20$ community banks include the ROA $(\%),$ the efficiency ratio $(\%),$ as a measure of bank productivity $($the lower the efficiency ratio, the better$),$ and total risk$-$based capital $(\%),$ as a measure of capital adequacy. Complete parts $($a$)$ through $($g$)$ below.

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a$.$ State the multiple regression equation.

Let $x_{1i}$ represent the efficiency ratio $(\%)$ and let $x_{2i}$ represent the total risk$-$based capital $(\%).$

$($Round the constant to two decimal places as needed. Round the coefficients to four decimal place

Distribution Costs

$\backslash$table$[[,$Efficiency,Total Risk$-$Based$],[$ROA $(\%),$Ratio $(\%),$Capital $(\%)],[1\mathrm{.}45,49\mathrm{.}47,16\mathrm{.}03],[0\mathrm{.}78,69\mathrm{.}82,11\mathrm{.}35],[1\mathrm{.}20,54\mathrm{.}13,18\mathrm{.}14],[0\mathrm{.}98,60\mathrm{.}49,20\mathrm{.}27],[1\mathrm{.}35,51\mathrm{.}73,11\mathrm{.}92],[1\mathrm{.}03,68\mathrm{.}02,15\mathrm{.}60],[1\mathrm{.}12,62\mathrm{.}30,17\mathrm{.}88],[0\mathrm{.}93,63\mathrm{.}10,18\mathrm{.}65],[0\mathrm{.}81,77\mathrm{.}32,22\mathrm{.}86],[0\mathrm{.}39,82\mathrm{.}83,15\mathrm{.}49],[1\mathrm{.}51,49\mathrm{.}95,17\mathrm{.}75],[1\mathrm{.}18,56\mathrm{.}24,15\mathrm{.}72],[1\mathrm{.}17,58\mathrm{.}36,14\mathrm{.}52],[1\mathrm{.}15,63\mathrm{.}52,15\mathrm{.}18],[1\mathrm{.}06,59\mathrm{.}37,14\mathrm{.}06],[1\mathrm{.}04,39\mathrm{.}93,17\mathrm{.}04],[0\mathrm{.}77,75\mathrm{.}83,12\mathrm{.}24],[0\mathrm{.}97,63\mathrm{.}30,24\mathrm{.}93],[1\mathrm{.}04,64\mathrm{.}19,16\mathrm{.}98],[0\mathrm{.}99,68\mathrm{.}29,13\mathrm{.}38],[,,]]$

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