$1)($Use $3$ decimal places throughout$).$ The AquaBlue Aparrel company has a difficult

time predicting quarterly sales for its bathing suit line due to seasonality in product

sales. The manager would like you to analyze his data and forecast sales for the next

year. Using your forecast he will be able to plan ahead in purchasing the necessary

inventory.

The quarterly sales data is given in the table below:

Quarter Sales $$000$

Jan $0524$

Apr $0572$

July $0541$

Oct $0516$

Jan $0620$

Apr $0663$

July $0638$

Oct $0615$

Jan $0717$

Apr $0760$

July $0731$

Oct $0713$

$($a$)$ Develop the trend projection equation to forecast the bathing suit sales for the

next four seasons. What is the R$2$ value?

$($b$)$ What are the forecasts for the next four quarters? Write down the MAD.

$($c$)$ Next perform a Trend and Seasonal analysis for this data. What are the sea$-$

sonal indices for each season. Which season$($s$)$ exhibits the largest seasonal

affect? Give a plausible explanation.

$($d$)$ Write down the regression equation after de$-$seasonalizing the data. The slope

of the line is and the intercept is $.$

$($e$)$ What is the R$2$ value after de$-$seasonalizing the data. Compare with your

answer in part $($a$).$ Explain what has happened?

$($f$)$ What are the forecasts for the next four quarters? What is the MAD? Include

units in your answer.

$($g$)$ Which method do you prefer and why?