$\backslash$table$[[$Quarter$,$Orders $\frac{1,000s}{?}$ Year,$\backslash$table$[[$Average$],[$Demad per$],[$Quarter$]],\backslash$table$[[$Seasonal$],[$Index$]]],[1,2,3,4,5],[$Jan$-$Mar,$27\mathrm{.}50,28\mathrm{.}50,37\mathrm{.}50,42\mathrm{.}50,49\mathrm{.}50,,],[$Apr $-$ Jun,$26\mathrm{.}75,31\mathrm{.}75,34\mathrm{.}75,42\mathrm{.}75,44\mathrm{.}75,,],[$Jul$-$Sep,$29\mathrm{.}00,32\mathrm{.}00,41\mathrm{.}00,44\mathrm{.}00,48\mathrm{.}00,,],[$Oct$-$Dec,$27\mathrm{.}25,32\mathrm{.}25,42\mathrm{.}25,47\mathrm{.}25,53\mathrm{.}25,,]]$

a$.$ Calculate the overall average demad.

b$.$ Calculate the average demad per quarter in the space given in the above table.

c$.$ Calculate the seasonal index in the space given in the above table.

d$.$ Develop a linear trend line $($simple linear regression line$)$ forecast for each of the four seasons season for year $6.($Create a separate table as we did in the Chapter $15$ Assessment, then find the intercept and the slope of the trend line.$)$

e$.$ Draw a time$-$series plot with original data and the trend line.

f$.$ Calculate he Mean Squared Error $($MSE$)$ for the trend$-$line$-$only forc MSE

g$.$ Projection for quarters $1$ through $4$ of year $6$ using trend and seasonal index.

$\backslash$table$[[$Year $6-$ Jan$-$Mar,$],[$Year $6-$ Apr$-$ Jun,$],[$Year $6-$ Jul $-$ Sep,$],[$Tear $6-$ Oct$-$Dec,$]]$