The values of Alabama building contracts (in millions of dollars) for a 12-month period follow.(a) Construct a time series plot.400350300250200+O1234Month56What type of pattern exists in the data?7240 340 220 260 280 31089150-100The data appear to follow a seasonal pattern.The data appear to follow a cyclical pattern.The data appear to follow a trend pattern.O The data appear to follow a horizontal pattern.10500111201 2400350300250200-1501005000 1 2 3 4 534 5 6 7 8 9 10 11 12 13MonthTime SeriesValue(in $ millions)240340(b) Compare the three-month moving average forecast with the exponential smoothing forecast using a = 0.2. (Round youranswers to two decimal places.)22026028031021032025063207Month230220210 320 250 320 230 220de8 9 10 11 12 13r3-Month MovingAverage Forecast(in $ millions)400350+300250200+150-100+50+001010101000400 T3503000 1 2 3 4250+200+150+100+α = 0.2Forecast(in $ millions)50567Month001 2 3 4 567MonthHe8 9 10 11 12 138 9 10 11 12 13iWhich provides more accurate forecasts based on MSE?O Exponential smoothing is more accurate, since its MSE calculated over all of the forecasted months is larger than theMSE using the three-month moving average.The three-month moving average is more accurate, since its MSE is smaller than the MSE for exponential smoothingcalculated over all of the forecasted months.The three-month moving average is more accurate, since its MSE is larger than the MSE for exponential smoothingcalculated over all of the forecasted months.Exponential smoothing is more accurate, since its MSE calculated over all of the forecasted months is smaller than theMSE using the three-month moving average.(c) Using the more accurate approach from part (b), what is the forecast (in millions of dollars) for the next month? (Roundyour answer to the nearest million dollars.)$million.

The time series is the method where the observation depends on the time. The variable is time-dependent. It changes its value with respect to the time. The time series is mainly used for the forecast of the value. One of the methods used for forecast is exponential smoothing and the moving average method.The random variable under study is value of the building contract The data is collected for the month.The objective is to estimate the forecasted value.The data istYt124023403220426052806310721083209250103201123012220From Excel, the time-series plot is constructed asEnter month and data in the Excel sheetSelect the columns of month and .Go to Insert menu.click on the “Insert scatter” option.Select Scatter under Charts..The time series plot for the data is The correct option is a second-time series plot from the first row.The time series plot indicates the observation with constant mean so it is a horizontal pattern.The option data appears to follow a horizontal pattern that is correct.The other options are incorrect there is no seasonal, trend, or cyclic pattern in the data.The forecasted value from the three-yearly moving average method isthe forecast by exponential smoothing method isThe calculation table istYtForecast by moving average method(F_tm)Forecast by exponential smoothing(F_te)(Yt-F_tm)^2(Yt-F_te)^21240234024010000322026016004260266.666725244.44444645280273.3333253.644.44444696.966310253.3333258.883211.1112613.2547210283.3333269.1045377.7783493.2838320266.6667257.28322844.4443933.3979250280269.8266900393.092510320260265.861236002931.00411230296.6667276.6894444.4442179.86312220266.6667267.35122177.7782242.136Total22644.4430146.99The MSE of the moving average method is calculated asThe MSE of the exponential smoothing method isThe method with minimum MSE indicates the model is accurately forecast the observation than other method.The MSE of the moving average method is minimum than the exponential smoothing method which indicates the moving average is the better method to use for the forecast.The second option the three-month moving average is more accurate as the MSE of the moving average is smaller than the MSE of the exponential smoothing method.Other options are incorrect as they do not have a correct explanation for the conclusion.The three-month moving average method is used for forecasting than the exponential smoothing for the stated problem.The forecast for the next month by the more accurate method that is the moving average method isThe time series plot for the stated data is The time series plot indicates the equal mean.The fourth option is correct.The option data appears to follow a horizontal pattern that is correct.The forecasted value for the data by exponential smoothing and the moving average method istYtForecast by moving average method(F_tm)Forecast by exponential smoothing(F_te)1240234024032202604260266.66672525280273.3333253.66310253.3333258.887210283.3333269.1048320266.6667257.28329250280269.826610320260265.861211230296.6667276.68912220266.6667267.3512The MSE for both methods is The second option the three-month moving average method is more accurate as its MSE is smaller than the MSE of the exponential smoothing method.The forecast for the next month from the more accurate method is .