Task $3$ data set illustrates over a $22-$day period the daily amount of tweed produced at the Argyll Factory that operates Monday to Friday.

$($a$)$ Construct a suitable graph to display the figures for the period shown.

$($b$)$ Carry out time$-$series decomposition on the data set assuming a MULTIPLICATIVE model.

$($c$)$ Use the elements you have determined to

o $$Forecast$$ the fabric production for the full $22-$day period.

o Calculate the average $$error$$ value for the multiplicative model.

Please ensure that all working figures are presented to at least three decimal places

The results you have produced will be referred to in the examination that takes place at the end of the semester.

In the examination you will also be asked some questions in respect to an ADDITIVE model.

There will be $20$ marks allocated to the section in the examination.