$1.$ Consider an equation to explain salaries of CEOs in terms of annual firm sales, return on equity $($roe$,$ in percentage form$),$ and return on the firm$$s stock $($ros$,$ in percentage form$)$

$($i$)$ In terms of the model parameters, state the null hypothesis that, after controlling for sales and roe, ros has no effect on CEO salary. State the alternative that better stock market performance increases a CEO$$s salary.