A company that sells mu cal Instruments has been in business for five years. During that time, sales of planes Increased from 13 units In the first year to 76 units In the most re at of plano sales for the mming year. The quarterly sales data follow. Year Quarter 1 | Quarter 2 | Quarter 3 Quarter 4 Total Yearly Sales 13 28 11 16 35 12 22 50 (2) e the data. (Round your answers to four dedmal places.) Year Quarter Adjusted Sales Seasona Deseasonalized Index Sales 1.2940 0.6097 0.4909 1.6054 1.2940 0.6097 0.4909 14 1.6054 11 1.2940 0.6097 3 0.4909 16 1.6054 12 1.2940 0.6097 4 0.4909 22 1.6054 18 1.2940 10 0.6097 5 13 0.4909 35 1.6054 Use the dese series to identify the trend. (Let t - 1 denote the tim value in quarter 1 of year 1; t - 2 denote the time series value in quarter 2 of year 1; ... and t - 20 denote the time series value in quarter 4 of year 5. Round your numerical values to two dedmal places.) T, - (b) Use the results of part (a) to develop a quarterly forecast for next year based on s to two decimal places.) forecast for quarter 1 forecast for quarter 2 forecast for quarter 3 forecast for quarter 4 (c) Use the adjusted s given in part (a) to a scast for quarter 1 the effect of season. (Round your answers to one decimal place) forecast for quarter 2 forecast for quarter 3 forecast for quarter 4Year Quarter Sales Adjusted Seasonal Index Deseasonalized Sales 1 1 2 1.2940 2/1.2940 = 1.5450 1 2 s 0.6097 5/0.6097 = 8.2006 1 3 4 0.4099 4/0.4099 = 9.7572 1 4 2 1.6054 2/1.6054 = 1.2459 2 1 4 1.2840 4/1.2940 = 3.0911 2 2 6 0.6097 6/0.6097 = 9.8407 2 3 9 0.4099 9/0.4099 = 21.9566 2 4 5 1.6054 5/1.6054 = 3.1144 B 1 s 1.2940 5/1.2940 = 3.8634 3 2 11 0.6097 11/0.6097 = 18.0478 B 3 13 0.4099 13/0.4099 = 31.7121 3 4 7 1.6054 7/1.6054 4.3502 4 1 18 1.2940 18,/1.2940 = 13.9098 4 2 13 0.6097 13/0.6097 21.3203 4 3 9 0.4099 9/0.4009 = 21.9566 4 4 16 1.6054 16,/1.6054 9.9675 5 1 22 1.2940 22/1.2940 = 17.0086 5 2 19 0.6097 19/0.6097 31.1585 5 3 20 0.4099 20/0.4099 = 48.7948 5 4 15 1.6054 15/1.6054 = 9.3420 Step (b): Identify the Trend and Forecast 1. Determine the Trend Equation: Fit a linear regression model to the deseasonalized data. The trend equation can be expressed as: T, =a+bt where a is the intercept and b is the slope. Using a linear regression on the deseasonalized sales data with time (from 1 to 20), you can calculate a and b. Step (c): Adjust the Forecast for Seasonality Use the seasonal indices to adjust the forecast for seasonality. To proceed with the trend analysis and forecast, | will need to calculate the trend using a linear regression. Let's first calculate the time series index (T) for each data point: Time Series Index (T) Year 1: 1,2,3,4 Year 2: 5,6,7,8 Year 3: 9,10,11,12 Year 4: 13,14, 15,16 Year 5: 17,18, 19,20 Now, we'll perform a linear regression on the deseasonalized sales data to find the trend equation and then use it to forecast the next year's sales. Let's move on to this calculation. The trend equation for the deseasonalized sales data is: T, =1.7712 + 1.2132 Using this trend equation, we can forecast the deseasonalized sales for the next year's four quarters (time indices 21 to 24): Quarter 1 (t = 21): 27.2481 Quarter 2 (t = 22): 28.4612 Quarter 3 (t 23): 29.6744 Quarter 4 (t = 24): 30.8876 Step (c): Adjust the Forecast for Seasonality Now, we will adjust these forecasts using the seasonal indices provided. 1. Forecast for Quarter 1: Adjusted Forecast 27.2481 x 1.2940 35.2738 2. Forecast for Quarter 2: Adjusted Forecast 28.4612 x 0.6097 17.3524 3. Forecast for Quarter 3: Adjusted Forecast 29.6744 x 0.4099 12.1701 4. Forecast for Quarter 4: Adjusted Forecast 30.8876 x 1.6054 49.6115 Summary of Forecasts for Next Year * Quarter 1: 35.2738 Quarter 2: 17.3524 e Quarter 3:12.1701 Quarter 4: 49,6115 These are the forecasts for the coming year, adjusted for seasonality