What is the forecast for July based on a three$-$month weighted moving average applied to the following past demand data and using the weights $5,3,$ and $2($largest weight is for most recent data$)?$ Show all of your computations for April through July.

Month

Demand

Forecast

January

$40$

February

$45$

March

$57$

April

$60$

May

$75$

June

$87$

July

$1$

$15\mathrm{.}0$

$2$

$16\mathrm{.}2$

$3$

$17\mathrm{.}1$

$4$

$18\mathrm{.}1$

$5$

$18\mathrm{.}8$

$6$

$19\mathrm{.}2$

$7$

$20\mathrm{.}5$

$$

a$.$ Use regression analysis to obtain an expression for the linear trend component.

b$.$ Forecast John's income for the next five years.