Consider the following time series data. \[\begin{array} { | c | c | } \hline \text { Year } & \text { Value } \\ \hline 1 & 234 \\ \hline 2 & 287 \\ \hline 3 & 255 \\ \hline 4 & 310 \\ \hline 5 & 298 \\ \hline 6 & 250 \\ \hline 7 & 302 \\ \hline 8 & 267 \\ \hline 9 & 225 \\ \hline 10 & 336 \\ \hline \end{array}\] a. Construct a time series plot. What type of pattern exists in the data? b. Develop a three-year moving average for this time series. Compute MSE and a forecast for the year 11.

a. @#IMG-DLM& The time series data appea

The monthly sales (in hundreds of dollars) of a company are listed below. \[\begin{array} { | c | c | } \hline \text { Month } & \text { Sales } ( \mathbf { \$ 1 0 0 s } ) \\ \hline \text { January } & 12,354 \\ \hline \text { February } & 13,657 \\ \hline \text { March } & 14,536 \\ \hline \text { April } & 13,478 \\ \hline \text { May } & 16,590 \\ \hline \text { June } & 19,790 \\ \hline \text { July } & 17,987 \\ \hline \text { August } & 18,657 \\ \hline \text { September } & 19,765 \\ \hline \text { October } & 18,678 \\ \hline \text { November } & 20,678 \\ \hline \text { December } & 23,675 \\ \hline \end{array}\] a. Construct a time series plot. What type of pattern exists in the data? b. Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series. c. What is the sales forecast (in hundreds of dollars) for next month?

a. @#IMG-DLM& The time series plot shows a linear

The following data shows the quarterly profit (in thousands of dollars) made by a particular company in the past 3 years. \[\begin{array} { | c | c | c | } \hline \text { Year } & \text { Quarter } & \text { Profit (\$1000s) } \\ \hline 1 & 1 & 45 \\ \hline 1 & 2 & 51 \\ \hline 1 & 3 & 72 \\ \hline 1 & 4 & 50 \\ \hline 2 & 1 & 49 \\ \hline 2 & 2 & 45 \\ \hline 2 & 3 & 79 \\ \hline 2 & 4 & 54 \\ \hline 3 & 1 & 42 \\ \hline 3 & 2 & 58 \\ \hline 3 & 3 & 70 \\ \hline 3 & 4 & 56 \\ \hline \end{array}\] a. Use α = 0.3 to compute the exponential smoothing values for the time series. Compute MSE and the forecast of profit (in $1000s) for the next quarter. b. Compare the three-period moving average forecast with the exponential smoothing forecast using α = 0.3. Which appears to provide the better forecast based on MSE?

a. Smoothing constant α = 0.3 @#IMG-DLM& MSE = 2,1

A) provide evidence of a causal relationship between an independent variable and the variable to be forecast. B) use the average of the most recent data values in the time series as the forecast for the next period. C) occur whenever all the independent variables are previous values of the same time series. D) relate a time series to other variables that are believed to explain or cause its behavior. A) provide evidence of a causal relationship between an independent variable and the variable to be forecast. B) use the average of the most recent data values in the time series as the forecast for the next period. C) occur whenever all the independent variables are previous values of the same time series. D) relate a time series to other variables that are believed to explain or cause its behavior.

The following times series shows the demand for a particular product over the past 10 months. \[\begin{array} { | c | c | } \hline \text { Month } & \text { Value } \\ \hline 1 & 324 \\ \hline 2 & 311 \\ \hline 3 & 303 \\ \hline 4 & 314 \\ \hline 5 & 323 \\ \hline 6 & 313 \\ \hline 7 & 302 \\ \hline 8 & 315 \\ \hline 9 & 312 \\ \hline 10 & 326 \\ \hline \end{array}\] a. Use α = 0.2 to compute the exponential smoothing values for the time series. Compute MSE and a forecast for month 11. b. Compare the three-month moving average forecast with the exponential smoothing forecast using α = 0.2. Which appears to provide the better forecast based on MSE?

a. Smoothing constant α = 0.2 @#IMG-DLM& MSE = 967

A) takes a positive value when the forecast is too high. B) cannot be negative. C) cannot be zero. D) is associated with measuring forecast accuracy. A) takes a positive value when the forecast is too high. B) cannot be negative. C) cannot be zero. D) is associated with measuring forecast accuracy.