In their study of the demand for international reserves $($i$.$e$.,$ foreign reserve currency such as the dollar or International Monetary Fund $[$IMF$]$ drawing rights$),$ Mohsen Bahami$-$oskooee and Margaret Malixi obtained the following regression results for a sample of $28$ less developed countries $($LDC$)$:

$\mathrm{????}\mathrm{????}(\frac{\mathrm{????}}{\mathrm{????}})=0\mathrm{.}1223+0\mathrm{.}4079\mathrm{????}\mathrm{????}(\frac{\mathrm{????}}{\mathrm{????}})+0\mathrm{.}5040\mathrm{????}\mathrm{????}{\mathrm{????}}_{\mathrm{????}\mathrm{????}}-0\mathrm{.}0918\mathrm{????}\mathrm{????}{\mathrm{????}}_{\mathrm{????}\mathrm{????}}$

$\mathrm{????}=(2\mathrm{.}5128)(17\mathrm{.}6377),(15\mathrm{.}2437)(-2\mathrm{.}7449)$

$\mathrm{????}2=0\mathrm{.}8268$

$\mathrm{????}=1151$

$\mathrm{????}=1120$

where $\mathrm{????}=$ the level of nominal reserves in U$.$S$.$ dollars

$\mathrm{????}=$ U$.$S$.$ implicit price defiator for GNP

$\mathrm{????}$ the nominal GNP in U$.$S$.$ dollars

ofII the variability measure of balance of payments

${\mathrm{????}}_{\mathrm{????}\mathrm{????}}=$ the variability measure of exchange rates

$($Nofes: The figures in parentheses are $1$ ratios. This regression was based on guarterly data from $1976$ to $1985(40$ quarters$)$ for each of the $28$ countries, giving a total sample size of $1120.)$

a$.$ A priori, what are the expected signs of the various coefficientsfi Are the $,$ results in accord with these expectationsfi

b$.$ What is the interpretation of the various partial slope coefficient?

c$.$ test the statistical Significance of each Estimated partial regression coefficient$($that is the null hypothesis is that Individually each true or cooperation regression coefficient is equal to zero$)$

d$)$ how would you test the hypothesis that all parts are sLOpe coefficients simultaneously zero?