# (8 hours enforced time limit) Question 1. The following table shows quarterly

(8 hours enforced time limit)
Question 1. The following table shows quarterly data of sales in billion dollars for five years 2016-2020 for a company.
YrQtr
Q1
Q2
Q3
Q4
2016
10
14
8
25
2017
16
22
14
35
2018
20
30
19
42
2019
26
34
24
50
2020
34
40
30
55
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 = 0.4. 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 comment.
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
15.4
30.0
18
2
11.7
28.0
15
3
12.4
32.5
25
4
10.8
39.0
20
5
9.4
40.9
10
6
6.5
50.8
16
7
10.0
40.1
5
8
9
10
9.5
9.0
8.3
50.5
45.0
48.0
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 se? 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.