Questions $16$ through $20$ The below table shows income $($in thousand dollars$)$ of $21$ workers at

different ages $($in years$)$ in a big company. Moreover, ${\displaystyle \underset{?}{\overset{?}{}}}{x}_i{y}_i=21198\mathrm{.}31.$

Fit a simple regression model to relate the income and the age of workers. Find the slope ${}_1$ and

the y$-$intercept ${}_0.$

$($A$){}_1=-0\mathrm{.}0324$;${}_0=39\mathrm{.}3516$

$($B$){}_1=-0\mathrm{.}2324$;${}_0=38\mathrm{.}7516$

$($C$){}_1=0\mathrm{.}5676$;${}_0=40\mathrm{.}0516$

$($D$){}_1=1\mathrm{.}1676$;${}_0=39\mathrm{.}0516$

$($E$){}_1=0\mathrm{.}4676$;${}_0=39\mathrm{.}1516$

Consider a worker of $28$ years old in this company, find his expected salary.

$($A$)57$

$($B$)61\mathrm{.}5$

$($C$)58$

$($D$)52$

$($E$)58\mathrm{.}5$

Estimate the variance of the random errors.

$($A$)1\mathrm{.}1528$

$($B$)0\mathrm{.}8908$

$($C$)1\mathrm{.}0908$

$($D$)1\mathrm{.}3438$

$($E$)1\mathrm{.}3448$

Construct a $99\%$ two$-$sided confidence interval for the the slope of the regression line.

$($A$)-0\mathrm{.}3124,1\mathrm{.}1977$

$($B$)-0\mathrm{.}0924,0\mathrm{.}7377$

$($C$)0\mathrm{.}0476,1\mathrm{.}1377$

$($D$)0\mathrm{.}2176,0\mathrm{.}7177$

$($E$)-0\mathrm{.}2524,0\mathrm{.}7477$

Determine the coefficient of determination:

$($A$)0\mathrm{.}6011$

$($B$)0\mathrm{.}0611$

$($C$)0\mathrm{.}6111$

$($D$)0\mathrm{.}5011$

$($E$)0\mathrm{.}5611$