The monthly sales for Yazici Batteries, Inc., were as follows:

MONTH	SALES
January	20
February	21
March	15
April	14
May	13
June	16
July	17
August	18
September	20
October	20
November	21
December	23

Forecast January sales using each of the following:

i) Naive method.

ii) A 3-month moving average.

iii) A 6-month weighted average using .1, .1, .1, .2, .2, and .3, with the heaviest weights applied to the most recent months.

iv) Exponential smoothing using an $\alpha=.3$ and a September forecast of 18.

v) A trend projection.

The monthly sales for Yazici Batteries, Inc., were as follows.

$$\begin{array}{|c|c|} \hline \text{MONTH} & \text{SALES} \\ \hline \hline \text{January} & 20 \\ \text{February} & 23 \\ \text{March} & 17 \\ \text{April} & 15 \\ \text{May} & 11 \\ \text{June} & 15 \\ \text{July} & 17 \\ \text{August} & 18 \\ \text{September} & 19 \\ \text{October} & 21 \\ \text{November} & 21 \\ \text{December} & 23 \\ \hline \end{array}$$

Plot the monthly sales data.

The monthly sales for Yazici Batteries, Inc., were as follows:

$$\begin{array}{|c|c|} \hline \text{MONTH}& \text{SALES}\\ \hline \text{Jan} & 20\\ \hline \text{Feb} & 21\\ \hline \text{Mar} &15\\ \hline \text{Apr} & 14\\ \hline \text{May}& 13\\ \hline \text{Jun}&16\\ \hline \text{Jul}&17\\ \hline \text{Aug} &18\\ \hline \text{Sep}&20\\ \hline \text{Oct}&20\\ \hline \text{Nov}&21\\ \hline \text{Dec}&23\\ \hline \end{array}$$

a) Plot the monthly sales data.

b) Forecast January sales using each of the following:

• Naive method.

• A $3$-month moving average.

• A $6$-month weighted average using $.1, .1, .1, .2, .2$, and $.3$, with the heaviest weights applied to the most recent months.

• Exponential smoothing using an $\alpha = 0.3$ and a September forecast of $18$.

The monthly sales for Yazici Batteries, Inc., were as follows:

$$\begin{array}{|c|c|} \hline \text{MONTH}& \text{SALES}\\ \hline \text{Jan} & 20\\ \hline \text{Feb} & 21\\ \hline \text{Mar} &15\\ \hline \text{Apr} & 14\\ \hline \text{May}& 13\\ \hline \text{Jun}&16\\ \hline \text{Jul}&17\\ \hline \text{Aug} &18\\ \hline \text{Sep}&20\\ \hline \text{Oct}&20\\ \hline \text{Nov}&21\\ \hline \text{Dec}&23\\ \hline \end{array}$$

Use trend projection to forecast the next year's March sales.

As you can see in the following table, demand for heart transplant surgery at Washington General Hospital has increased steadily in the past few years:

The director of medical services predicted 6 years ago that demand in year 1 would be 41 surgeries.

Use the trend-projection method to forecast demand in years 1 through 6.

Mark Gershon, owner of a musical instrument distributorship, thinks that demand for guitars may be related to the number of television appearances by the popular group Maroon 5 during the previous month. Mark has collected the data shown in the following table:

Use the least-squares regression method to derive a forecasting equation.

The Carbondale Hospital is considering the purchase of a new ambulance. The decision will rest partly on the anticipated mileage to be driven next year. The miles driven during the past 5 years are as follows:

Forecast the mileage for next year (6th year) using a 2-year moving average.

Mark Gershon, owner of a musical instrument distributorship, thinks that demand for guitars may be related to the number of television appearances by the popular group Maroon 5 during the previous month. Mark has collected the data shown in the following table:

What is your estimate for guitar sales if Maroon 5 performed on TV nine times last month?

Lenovo uses the ZX-81 chip in some of its laptop computers. The prices for the chip during the past 12 months were as follows:

Which is better (using the mean absolute deviation): the 2-month average or the 3-month average?

As you can see in the following table, demand for heart transplant surgery at Washington General Hospital has increased steadily in the past few years:

The director of medical services predicted 6 years ago that demand in year 1 would be 41 surgeries.

Use a 3-year moving average to forecast demand in years 4,5 . and 6.

The actual demand for the patients at Omaha Emergency Medical Clinic for the first 6 weeks of this year follows:

Clinic administrator Marc Schniederjans wants you to forecast patient demand at the clinic for week 7 by using this data. You decide to use a weighted moving average method to find this forecast. Your method uses four actual demand levels, with weights of $0.333$ on the present period, $0.25$ one period ago, $0.25$ two peri= ods ago, and $0.167$ three periods ago.

What if the weights were $0.40,0.30,0.20$, and $0.10$, respectively? Now what is the forecast for week 7 ?

Lenovo uses the ZX-81 chip in some of its laptop computers. The prices for the chip during the past 12 months were as follows:

Compute the forecasts for each month using exponential smoothing, with an initial forecast for January of $\$ 1.80$. Use $\alpha$ $=.1$, then $\alpha=.3$, and finally $\alpha=.5$. Using MAD, which $\alpha$ is the best?

The following tabulations are actual sales of units for six months and a starting forecast in January. Calculate forecasts for the remaining five months using simple exponential smoothing with $\alpha=0.2$.

The following tabulations are actual sales of units for six months and a starting forecast in January. Calculate MAD for the forecasts.