Problem 15-05 (Algorithmic) Consider the following time series data. Week Value 1 16 2 12 3 14 4 13 5 15 6 14 a. Choose the correct time series plot. Time Series Value Time Series Value wm Week(t) Week(t) 2 3 4 23 (ii) (iv) Time Series Value Time Series Value 20 (iii) (iv) Time Series Value Time Series Value Week(t) 1 2 3 4 5 6 Week(t) 6 2 3 4 5 Plot (ii) What type of pattern exists in the data? Trend Pattern x b. Develop a three-week moving average for this time series. Compute MSE and a forecast for week 7. Round your answers to two decimal places. Time Series Week Forecast Value 16 5 6 15 14 MSE: 1.67 The forecast for week 7: 14 C. Use a = 0.2 to compute the exponential smoothing values for the time series. Compute MSE and a forecast for week 7. Round your answers to two decimal places. Time Series Week Forecast Value 16 16 15.2 14.96 14.57 14.65 x MSE: 5.47 x MSE: 5.47 x The forecast for week 7: 14.52 X d. Compare the three-week moving average forecast with the exponential smoothing forecast using a = 0.2. Which appears to provide the better forecast based on MSE? Exponential smoothing X Explain. The input in the box below will not be graded, but may be reviewed and considered by your instructor. e. Use trial and error to find a value of the exponential smoothing coefficient a that results in a smaller MSE than what you calculated for a = 0.2. Find a value of a for the smallest MSE. Round your answer to three decimal places. a = 0.5 x Feedback Check My Work Partially correct