Consider the following time series data. Quarter Year 1 Year 2 Year 3 1 2 5 7 N O N 6 W CO 10 4 5 8 10 (a) Choose the correct time series plot. (i) 12 10 Time Series Values Year 1. Year 1, Year 1. Year 1, Year 2. Year 2, Year 2, Year 2, Year 3, Year 3, Quarter 1 Quarter 2 Quarter 3 Quarter 4 Quarter 1 Quarter 2 Quarter 3 Quarter 4 Quarter 1 Quarter 2 Quarter ) Quarter 4 Year 3. Time Period (ii) 12 11 10 Time Series Values Year 1. Year 1, Year 1. Year 1, Year 2. Year 2, Year 2. Year 2, Year 3, Year 3, Year 3. Year 3, Quarter 1 Quarter 2 Quarter 3 Quarter 4 Quarter 1 Quarter 2 Quarter 3 Quarter & Quarter 1 Quarter 2 Quarter ) Quarter 4 Time Period(iii) 12 10 Time Series Values Year 1. Year 1, Year 1. Year 1, Year 2. Year 2, Year 2. Year 2, Year 3, Year 3, Quarter 1 Quarter 2 Quarter 3 Quarter 4 Quarter 1 Quarter 2 Quarter 3 Quarter & Quarter 1 Quarter 2 Quarter ) Quarter 4 Year 3. Year 3, Time Period (iv) 12 Time Series Values o Year 1. Year 1, Year 1. Year 1, Year 2. Year Z, Year 2. Year 2, Year 3, Year 3, Year 3. Year 3, Quarter 1 Quarter 2 Quarter 3 Quarter 4 Quarter 1 Quarter 2 Quarter 3 Quarter & Quarter 1 Quarter 2 Quarter ) Quarter 4 Time Period Plot (iv) What type of pattern exists in the data? Positive trend pattern, with seasonality , ) Use a multiple regression model with dummy variables as follows to develop an equation to account for seasonal effects in th data: Qtr1 = 1 if Quarter 1, 0 otherwise; Qtr2 = 1 if Quarter 2, 0 otherwise; Qtr3 = 1 if Quarter 3, 0 otherwise If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there a + sign before the blank (Example: -300). If the constant is "1" it must be entered in the box. Do not round intermediateb) Use a multiple regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data: Qtrl = 1 if Quarter 1, 0 othenNise; Qtr2 = 1 if Quarter 2, 0 otherwise; Qtr3 = 1 if Quarter 3, 0 otherwise. If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank (Example: 300). If the constant is "1" it must be entered in the box. Do not round intermediate calculation. p: 7.6667 + -3 Qtr1 + -5 Qtr2+ o Qtr3 c) Compute the quarterly forecasts for next year based on the model you developed in part (b). If required, round your answers to three decimal places. Do not round intermediate calculation. 4 2 2.667 4 3 7.667 4 4 7.667 d) Use a multiple regression model to develop an equation to account for trend and seasonal effects in the data. Use the dummy variables you developed in part (b) to capture seasonal effects and create a variable t such that t = 1 for Quarter 1 in Year 1, t = 2 for Quarter 2 in Year 1,... t = 12 for Quarter 4 in Year 3. If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank (Example: 300). )7= 2.4167 + -1.03125 Qtr1+ -3.6875 Qtr2+ 0.65625 Qtr3+ 0.65625 t (e) Compute the quarterly forecasts for next year based on the model you developed in part (d). Do not round your interim computations and round your final answer to three decimal places. Year Quarter Period 9.9167 7.9167 12.9167 12.9167 (f) Calculate the MSE for the regression models developed in parts (b) and (d). If required, round your intermediate calculations and final answer to three decimal places. Model developed in part (b) Model developed in part (d) Is the model you developed in part (b) or the model you developed in part (d) more effective? The model developed in - Select your answer - is more effective because it has the - Select your answer - MSE
