1. Sunglasses Sales Excellence Discussion

2. Sunglasses Identify and describe at least one further feature of this time series data with reasons. – Sunglasses sales show seasonal variation with sales being highest in December and lowest in September. Sales are significantly above the trendline for December quarters, below the trendline in March and September, and usually just above the trendline in June (except first value). – Sales are probably highest in December as this is the start of summer. They probably increase a bit in June as people may need sunglasses for reducing the glare of the snow while skiing. Then sales decrease until summer begins. – Appears to be a change in trend at March 2003 where sales are still increasing, but not as quickly. Perhaps there is an economic downturn and as sunglasses are a bit of a luxury item, perhaps less people are buying them.

3. Sunglasses Relevance and usefulness of forecasts. – The forecast for December 2006 would be more relevant as it is only one year in the future compared to the forecast for March 2008 which is more than 2 years in the future. It appears that the trend is changing and we can be less certain that our model is a good fit as we go further in the future. – The forecasts about the sales of sunglasses would be relevant to both manufacturers and sellers of sunglasses. Manufacturers would be able to better plan their productions in terms of materials and costs. Sellers would be able to place their orders in accordance with the increasing sales trend so that they were not short of stock.

4. Sunglasses Appropriateness of the model. – Although the linear model has a fairly high R 2 of 0.869, which indicates that it is quite a good fit for the data and therefore appropriate for making predictions, it appears that the data may actually show two separate trends and might be better represented by two linear models. It seems that the sales of sunglasses, although still increasing, is not increasing as fast after March 2003. – A linear model is limited in usefulness because if we try to predict far into the future, it will make higher and higher predictions and there has to be a point where sunglasses sales reach a maximum as there are only so many people to buy them. The trend cannot continue to increase indefinitely.

5. Sunglasses Possible improvements. – When I split the data, both new trendlines appear to fit the data quite well, following the points much more closely. In fact, the first trendline up to March 2003 fits the data almost perfectly with a R 2 of 0.999. However, the other trendline does not have as high of an R 2 (0.727) as the original trendline showing that perhaps this trendline is not as good as our original one for predicting values at this end of the data and therefore may not be as good for making predictions about the future.

6. Sunglasses Possible improvements. (continued) – As we only have a few years of data being used in the model for the new trendline, it is somewhat unclear exactly what the new trend is, and having more data would allow us to establish a more reliable trendline for predicting future sales.

7. Sunglasses Limitations of the analysis. – The predictions made assume that both the overall trend and the average seasonal effects will continue unchanged. – Using moving means in our model means that equal weighting is given to data at the beginning of the period and at the end. Since it seems like there is a change in the trend of sunglasses sales, perhaps we should give more weighting to the more recent data. – Having more data available would allow us to identify if the apparent change in the trend continues in the future or perhaps is part of a longer cyclical effect.

8. Sunglasses Interpretation of the seasonally adjusted data. – Looking at the seasonally adjusted values and the graph of the CMM and the SAV, there are a couple of values which are below what is expected (June 2001 and Dec 2004). As the SAV have the seasonal effects removed, this must be due to some unusual event. Perhaps the periods of June 2001 and December 2004 had extremely rainy weather so people were not buying sunglasses as much as expected. Dec 2002 and June 2005 had values which were higher than expected, which could have been due to unusually sunny weather during these periods.