$(1)$ Taxi rides for the Hajj months in Mecca, Saudi Arabia are closely linked to the number of pilgrims visiting each year. Below are the data obtained over the past $12$ years.

$\backslash$table$[[$Number of passengers $($in milions$),$Number of pilgrims $($in millions$),$year$],[1\mathrm{.}5,7,1],[1\mathrm{.}0,2,2],[1\mathrm{.}3,6,3],[1\mathrm{.}5,4,4],[2\mathrm{.}5,14,5],[2\mathrm{.}7,15,6],[2\mathrm{.}4,16,7],[2\mathrm{.}0,12,8],[2\mathrm{.}7,14,9],[4\mathrm{.}4,20,10],[3\mathrm{.}4,15,11],[1\mathrm{.}7,7,12]]$

$(1)$ Plot this data and determine whether$-$a linear$-$model is reasonable.

$(2)$ What is the simple linear regression relationship equation?

$(3)$ What is the expected number of passengers if $10$ million pilgrims visit Mecca in a year?

$(4)$ Explain the number of passengers expected in answer $(3)$ if there are no pilgrims at all?

The White Thob Company, based in Saudi Arabia, uses metal buttons in some of its designs. It was price A set of $10$ buttons for the past $12$ months is as follows:

$\backslash$table$[[$Group price $($SAR$),$City,Group price $($SAR$),$City$],[1\mathrm{.}80,$July,$1\mathrm{.}80,$Janusy$],[1\mathrm{.}83,$August,$1\mathrm{.}67,$February$],[1\mathrm{.}70,$Seplember,$1\mathrm{.}70,$March$],[1\mathrm{.}65,$October,$1\mathrm{.}85,$A$.$pril$],[1\mathrm{.}70,$November,$1\mathrm{.}90,$May$],[1\mathrm{.}75,$December,$1\mathrm{.}87,$June$]]$

$(1)$ Use the $2-$month simple moving average on all data and plot averages and prices. $(2)$ Use the $3-$month simple moving average and add the $3-$month chart to the chart created in Part $(1)(3)$ Which is better, the $2-$month average or the $3-$month average? And why?