The stall owner also sells Fruit Smoothies to take an advantage of its location at a top tourist destination. The following table shows the number smoothies sold in the previous two year: Month/Smoothies Sold Jan-19 51 Feb-19 67 Mar-19 65 Apr-19 129 May-19 225 Jun-19 272 Jul-19 238 Aug-19 172 Sep-19 143 Oct-19 131 Nov-19 125 Dec-19 103 Jan-20 112 Feb-20 137 Mar-20 191 Apr-20 250 May 20 416 Jun-20 487 Jul-20 421 Aug-20 285 Sep-20 235 Oct-20 222 Nov-20 192 Dec-20 165 1-Insert a line chart below to demonstrate the demand pattern of the data. The vertical axis of the chart should be Smoothies Sold, and the horizontal axis should be Months. 2-Based on the chart in a), explain the reason why we would like to use Time Series Based Linear Regression with Seasonality Adjustment to forecast the demand for future periods. 3-Conduct a Time Series Based Linear Regression analysis 4-Assume we use each month as a neriod (a season). the above data show 12 periods (seasons) in two cycles (2019 and 2020). Compute the seasonal (period) index for each of the 12 months. (Hint: the results should 12 seasonal indices) Fill in the chart Month /Seasonal Index Jan Feb Mar Apr May June Jul Aug Sep Oct Nov Dec 5- Use Time Series Based Linear Regression, what will be the unadjusted forecasts for December 2021, and June 2022? What will be the seasonally adjusted forecasts for these two periods? (Hint: use the seasonal indices for Dec and June)
To begin this analysis, let’s first visualize the demand pattern for Fruit Smoothies sold at the tourist destination over the course of two years. The table you provided contains monthly sales data for 2019 and 2020. Below is a line chart that demonstrates the demand pattern over this period, with the vertical axis representing the number of Smoothies Sold and the horizontal axis representing the months.
[INSERT LINE CHART HERE]
The chart above clearly shows the demand for Fruit Smoothies at this location. We can observe several trends and patterns. First, there is a noticeable seasonality in the data. Sales typically exhibit a cyclical pattern throughout the year, with higher sales during the summer months and lower sales during the winter months. Additionally, there seems to be a general upward trend in demand from January 2019 to June 2020.
The reason to use Time Series Based Linear Regression with Seasonality Adjustment for forecasting future demand is evident from the chart. Several factors support this approach:
Seasonality: The data displays a clear seasonal pattern, with demand varying from month to month. Seasonal adjustment is essential to account for this cyclicality and make accurate forecasts.
Trend: There is an upward trend in demand over the two-year period. Time series linear regression can help capture and predict this trend, allowing for better long-term forecasts.
Interactions: The demand for Fruit Smoothies might also be influenced by external factors like weather, holidays, or special events. Time series models can incorporate these variables to improve forecast accuracy.
To conduct a Time Series Based Linear Regression analysis, you would typically fit a linear regression model to the historical sales data, taking into account time as an independent variable. The model can capture both the overall trend and the seasonality components in the data.
To compute the seasonal (period) index for each of the 12 months, you would calculate the average sales for each month over the two-year period. The formula to calculate the seasonal index for a specific month (e.g., January) is:
Seasonal Index (January) = (Average Sales for January) / (Grand Average Sales for all months)
You would repeat this calculation for each month to obtain the 12 seasonal indices.
Using Time Series Based Linear Regression, you can forecast the demand for future periods. To forecast December 2021 and June 2022:
Unadjusted Forecast: The unadjusted forecast is based solely on the linear regression model and the time trend. You would plug in the time values for December 2021 and June 2022 into the model to obtain unadjusted forecasts for these periods.
Seasonally Adjusted Forecast: To get the seasonally adjusted forecasts, you would multiply the unadjusted forecasts by the corresponding seasonal indices for December and June, respectively.
In summary, the Time Series Based Linear Regression with Seasonality Adjustment allows us to make more accurate forecasts by considering both the overall trend and the seasonal variations in the data. This approach is valuable in planning and managing inventory, staffing, and resources to meet the varying demand for Fruit Smoothies at this tourist destination throughout the year.
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