Question 1. The following table shows quarterly data of sales in billion dollars for five years 2016-2020 for a company.

Yr\Qtr	Q1	Q2	Q3	Q4
2016	30	40	25	75
2017	50	66	45	105
2018	70	110	75	150
2019	110	120	80	200
2020	150	200	140	300

Plot the data and comment on its time series features like trend, seasonality, etc. Apply the double moving average with four periods (DMA-4). Calculate the MPE and comment about systematic bias in forecasting. Also calculate the RMSE of in-sample forecasts. Forecast for the first two quarters of 2021 using DMA-4. Plot the DMA-4 forecast vs actual values and comment on the pattern of the forecasted time series plots. Also plot the errors of DMA-4 and comment.

Question 2. For the data in question 1 apply the Holt-Winters' triple smoothing (three parameter model) with alpha = 0.2, beta = 0.4 and gamma = 0.5. Calculate MPE and RMSE and compare with the results in Part (A). Forecast for the first two quarters of 2021. Plot the forecasted values vs. actual values as well as the errors and make comments.

Question 3. For the data in question 1 perform the Decomposition using Ratio-to-Moving average. Estimate the seasonal coefficients and the de-seasonalized series. Then estimate the Trend using Linear Regression. Finally Forecast for in-sample periods and the first two quarters of 2021. Calculate errors in forecast. Compare its RMSE with the results above. Plot the errors and comment.

Question 4. It was felt by the local utility company that fuel consumption (natural gas) in their small town would be affected by temperature and chill index. The following data was collected for 10 weeks during the winter.

Week	Fuel Consumption Y(MMcf)	Average Temp X1 (0F)	Chill Index X2
1	15	30.0	18
2	12	28.0	15
3	12.5	32.5	25
4	11	39.0	20
5	9	41	10
6	7	51	16
7	10	40	5
8 9 10	9.5 9 8	50.5 45.0 50	0 10 8

Conduct a Multiple Regression among Fuel consumption (Y), temperature (X₁), and chill index (X₂). Solve using excel. What is the multiple regression equation? Interpret the coefficients and predict the fuel consumption when temperature is 35 degrees, and the chill index is 12. Are the coefficients of the multiple regression model statistically significant at alpha = 0.05 and 0.01? How do you know?Discuss indicating the individual test statistics and p-values. What are R², adjusted R² and s_e? Interpret R² and Adjusted R² and compare these values. Perform F-test, show the ANOVA table and conclude about the overall statistical significance of the model.