Question

Case Study Forecasting Monthly Sales For years The Glass Slipper restaurant has operated in a resort shore. They also knew that hiring the right manager would al- community near a popular ski area of New Mexico. The restau low James and Deena the time to begin a semi-retirement in a rant is busiest during the first 3 months of the year, when the corner of paradise. ski slopes are crowded and tourists flock to the area. To make this happen, James and Deena would have to sell When James and Deena Weltee built The Glass Slipper, they had a vision of the ultimate dining experience. As the view of surrounding mountains was breathtaking, a high priority was placed on having large windows and providing a spectacular view from anywhere inside the restaurant. Special attention was also given to the lighting, colors, and overall ambiance, result- ing in a truly magnificent experience for all who came to enjoy gourmet dining. Since its opening, The Glass Slipper has devel- oped and maintained a reputation as one of the "must visit" The Glass Slipper for the right price. The price of the business would be based on the value of the property and equipment, as as projections of future income. A forecast of sales for the next year is needed to help in the determination of the value of the restaurant. Monthly sales for each of the past 3 years are provided in Table 5.14 Discussion Questions 1. Prepare a graph of the data. On this same graph, plot a places in that region of New Mexico 12-month moving average forecast. Discuss any apparent trend and seasonal patterns. While James loves to ski and truly appreciates t he moun- tains and all that they have to offer, he also shares Deena's dream of retiring to a tropical paradise and enjoying a more relaxed lifestyle on the beach. After some careful analysis of their financial condition, they knew that retirement was many years away. Nevertheless, they were hatching a plan to bring them closer to their dream. They decided to sell The Glass Slipper and open a bed and breakfast on a beautiful beach in Mexico. While this would mean that work was still in their future, they could wake up in the morning to the sight of the palm trees blowing in the wind and the waves lapping at the 2. Use regression to develop a trend line that could be used to forecast monthly sales for the next year. Is the slope of this line consistent with what you observed in question 1? If not, discuss a possible explanation. 3. Use the multiplicative decomposition model on these data. Use this model to forecast sales for each month of the next year. Discuss why the slope of the trend equation with this model is so different from that of the trend equa tion in question 2. TABLE 5.14 Monthly Revenue (in $1,000s) MONTH January February March 438 420 414 318 306 240 240 425 423 331 318 245 255 223 210 233 278 322 2010 450 438 434 338 May une July August September October November December 254 264 231 224 243 289 335 225 270 315

Answer 1

1) Time series plot of revenue as function of time is shown below

50 1 2 3 456 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 Time period (t) \r\nSimple Linear Repression (Least Squares Repression Method 438 420 414 318 306 240 438 840 1242 1272 1530 1440 680 1728 1782 2250 2970 3780 5772 5950 6345 5296 5406 4410 4845 4460 4410 5126 6394 7728 11250 11388 216 198 225 270 315 100 121 144 169 196 225 256 425 423 331 245 255 223 324 361 400 233 278 322 450 438 434 338 331 484 529 576 625 676 729 231 224 243 289 335 11138 9464 9599 7620 8184 7392 7392 8262 10115 12060 201538 900 961 1024 1089 1156 1225 1296 16206 Regression Equation: yabx, where x Price (independent variable) y Number Sold (dependent variable) a - intercept point of regression line and y-axis b -slope of regression line 16206 443556 201538 11138 y= (N ???-????)--1.16 0 Intercept (a) - (y bx330.85 Regression Equation: y: 330.85 +-1.16x \r\n1 Multiplicative Decomposition tercept292.792 Slope0.5160 Averag 304.458 PeriodMonthly Seasonal Deseasonal 5 Year Month (t)Revenue (At) Ratio Indexdata Trend Forecast 6 2008 Jan 1.441.46 300.3 18 414 318 1.041.08 1.011.05 12 288.8 ?.fl. ?.in ?. 0.69 ??2 ?// 315 1.46 1.46 1.40 304.5 302.6 304.0 306.3 304.1 302.8 306.9 304.0 303.5 303.6 303.4 302.6 308.6 1.40 300.0 300.5 301.0 301.6 302.1 302.6 303.1 303.6 304.1 304.7 305.2 305.7 306.2 Mar 423 38 318 May 17 Jun ? 0.73 0.73 26 21 278 0.92 322 1.48 %2 312.8 ? isi 313.9 1.11 307.2 igll/.? 308.3 308.8 309.3 309.8 310.3 Mi 29 224 243 0.74 0.80 0.95 0.92 323.7 316.6 34 35 Dec 314.8 311.4 42 2011 Jan 38 39 312.4 438.8 312.9 435.4 313.4 338.7 313.9 328.3 314.5 254.4 315.0 261.7 315.5 231.4 316.0 218.7 316.5 242.9 317.0 290.5 317.6 337.9 42 46 "",""error"":null,""modified"":1551899617,""source"":""automated""}"

Trend: the time series plot shows that there is a slightly increasing trend.

Seasonality: There is a clear seasonal pattern evident in the time series plot. Monthly revenue is the highest in Jan month and then it decreases until Sep, after which it again increases until Jan. The rate of decrease and increase is identical year after year.

2) Regression to develop trend line.

The trend line developed using regression shows a downward slope. That is possible because the rate of decrease is becoming steeper, and rate of increase is getting flatter.

3) Multiplicative decomposition.

Formulas:

D3 =AVERAGE(D6:D29)

G2 =INTERCEPT($G$6:$G$29,$C$6:$C$29)

G3 =SLOPE($G$6:$G$29,$C$6:$C$29)

E6 =D6/$D$3 copy to E6:E41

F6 =AVERAGE(E6,E18,E30) copy to F6:F17

F18 =F6   copy to F18:F53

G6 =D6/F6   copy to G6:G41

H6 =$G$2+$G$3*C6   copy to H6:H53

I42 =H42*F42   copy to I42:I53