For years The Glass Slipper restaurant has operated in a resort community near a popular ski area of New Mexico. The restaurant is busiest during the first 3 months of the year, when the ski slopes are crowded and tourists flock to the area. 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, resulting in a truly magnificent experience for all who came to enjoy gourmet dining. Since its opening, The Glass Slipper has ...view middle of the document...
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 equation in question 2.
The scatter plot of the data shows a definite seasonal pattern with higher sales in the winter months and lower sales in the summer and fall months. There is a slight upward trend as evidenced by the fact that for each month, the sales increased from the first year to the second, and again form the second year to the third.
2. A trend line based on the raw data is found to be:
Y = 330.889 – 1.162X
The slope of the trend line is negative which would indicate that sales are declining over time. However, as previously noted, sales are increasing. The high seasonal index in January and February causes the trend line on the unadjusted data to appear to have a negative slope.
3. There is a definite seasonal pattern and a definite trend in the data. Using the decomposition method in QM for Windows, the trend equation (based on the deseasonalized data) is
Y = 294.069 + 0.859X
The table below gives the seasonal indices, the unadjusted forecasts found using the trend line, and the final (adjusted) forecasts for the next year.
Month Unadjusted forecast Seasonal index Adjusted forecast
January 325.852 1.447 471.5
February 326.711 1.393 455.1
March 327.57 1.379 451.7
April 328.429 1.074 352.7
May 329.288 1.039 342.1
June 330.147 0.797 263.1
July 331.006 0.813 269.1
August 331.865 0.720 238.9
September 332.724 0.667 221.9
October 333.583 0.747 249.2
November 334.442 0.891 298.0
December 335.301 1.033 346.4