$5$ In the linear consumption function

widehat$($ cons $)=$hat$({)}_0+$hat$({)}_1$ inc,

the $($estimated$)$ marginal propensity to consume $($MPC$)$ out of income is simply the slope, hat$({)}_1,$ while the average propensity to consume $($APC$)$ is widehat$\frac{\text{c}\text{o}\text{n}\text{s}}{?}$ inc $=$hat$\frac{({)}_0}{?}$ inc $+$hat$({)}_1.$ Using observations for $100$ families on annual income and consumption $($both measured in dollars$),$ the following equation is obtained:

widehat$($ cons $)=-124\mathrm{.}84+0\mathrm{.}853$ inc

$n=100,R^2=0\mathrm{.}692.$

$($i$)$ Interpret the intercept in this equation, and comment on its sign and magnitude.

$($ii$)$ What is the predicted consumption when family income is $$30,000?$

$($iii$)$ With inc on the $x-$axis, draw a graph of the estimated MPC and APC.