The Badrutt$$s Palace Hotel St$.$ Moritz which is one of the best Alpine hotels in Switzerland has provided you with their quarterly bookings data over the last $6$ years as follows:

Year Quarter$-1$

$($Demand in units$)$ Quarter$-2$

$($Demand in units$)$ Quarter$-3$

$($Demand in units$)$ Quarter$-4$

$($Demand in units$)$

$201745,00022,00064,00033,000$

$201848,00027,00074,00041,000$

$201952,00032,00083,00046,000$

$202057,00035,00094,00052,000$

$202161,00042,000104,00056,000$

$202267,00049,000120,00061,000$

Required:

i$)$ Calculate the seasonal indices for each season using multiplicative index $(3$ Marks$)$

ii$)$ Forecast the demand for each season of the year $2023$ given that the annual demand forecast is $324,000$ units. $(2$ Marks$)$

iii$)$ Deseasonalize the actual demand data $(2017-2022)$ above using the seasonal indices obtained in $($a$)$ above. $(2$ Marks$)$

iv$)$ Generate OLS equation using the Deseasonalized data in $($iii$)$ above $($in thousand units$)$

$(3$ Marks$)$