A division of climatic change is interested in analysing the pattern o

Question

A division of climatic change is interested in analysing the pattern of the CO2 concentrations in the air of a particular state in past years and then forecasting the CO2 concentrations for the upcoming years. The monthly mean CO2 concentrations ppm (parts per million) mixing ratio in dry air from January 2006 through December 2019 were recorded. The following monthly data are given in the following table for past 14 years:

Month	2006	2007	2008	2009	2010	2011	2012	2013	2014	2015	2016	2017	2018	2019
January	299.16	299.62	300.60	301.67	303.71	305.00	306.77	308.32	309.90	310.41	312.87	313.88	315.04	316.33
February	299.94	300.40	301.60	302.17	304.23	305.63	307.26	309.41	310.70	311.68	313.59	314.62	315.70	316.82
March	300.41	300.87	302.57	303.86	305.54	306.93	309.10	310.69	311.70	312.04	314.11	316.23	316.38	318.29
April	301.72	302.18	303.72	305.07	306.79	307.95	309.88	311.51	312.65	314.27	316.07	316.62	318.38	319.91
May	302.13	302.92	303.68	305.82	306.95	308.05	310.47	312.02	313.28	314.92	316.38	317.53	318.93	319.41
June	301.09	302.43	303.17	305.12	307.00	308.27	310.31	311.54	312.42	314.40	315.78	316.87	318.26	318.74
July	300.10	300.85	301.96	303.81	305.37	306.64	308.41	309.88	311.02	313.16	313.96	315.00	316.44	316.92
August	298.14	299.01	299.80	301.56	303.47	304.68	306.74	307.75	308.97	311.11	311.71	312.86	314.55	315.03
September	296.36	297.51	297.98	300.30	301.46	302.77	305.07	306.05	306.84	309.11	309.86	311.55	313.21	313.69
October	296.29	297.41	297.57	300.22	301.29	303.09	305.07	306.13	307.00	309.15	310.13	311.57	312.67	313.15
November	297.23	298.25	299.20	301.37	302.76	304.29	306.22	307.45	308.20	310.38	311.84	313.11	314.09	314.57
December	298.55	299.97	300.58	302.49	303.80	305.76	307.38	308.85	309.63	312.02	313.32	314.49	315.27	315.75

a) Compute the seasonal indices using ratio to moving average method.
b) Obtain the deseasonalised values and then fit a linear trend line to the average annual CO2 concentrations using least squares method.
c) Convert the annual least-squared trend equation to a monthly trend equation.
d) Use the monthly trend equation and seasonal indices to forecast the CO2 concentrations for all twelve months of 2021.
e) Plot the original data, deseasonalised data and trend values.

11 Mar 2022

Answer :

Word Count : 441

This is a time series analysis problem requiring seasonal adjustment, trend fitting, and forecasting. I'll follow these steps: 1. Compute Seasonal Indices using the Ratio to Moving Average Method 2. Obtain Deseasonalized Values 3. Fit a Linear Trend Line using Least Squares 4. Convert the Annual Trend to a Monthly Trend Equation 5. Forecast CO₂ Concentrations for 2021 6. Plot the Original Data, Deseasonalized Data, and Trend Values I'll start by processing the ___ ______ _____ ______ _________ ____ ___ ____ ____ __________.
____ _______ ___ ______ ______ ________ _____ _____ ______.
__________ _______ _____ ________ __________ ____ ________ __________.
_____ ____ __________ _____ __________ _____ ______ _______ ____ ___ ______ ________.
____ _____ _____ ________ __________ ____ _____ __________ _______ ____ ___.
__________ __________ __________ ______ __________ ____ ________ ________ _______ __________ _______.
_____ __________ _____ ________ _________ ________ __________ __________.
__________ ______ _________ __________ ___ _____ _____.
__________ ________ ________ ______ _________ __________ ________ ______.
___ ________ _________ ___ __________ ______ ________ _____ ____ ___.
________ ___ __________ _____ ____ _______ __________ ____ _______ _________.
_______ ___ ______ __________ ____ ____ _________ _____.
_________ _______ ______ __________ _______ ____.
_______ _______ __________ ____ _______ _________ ________ __________ ____ ___.
_____ ________ ___ _____ __________ _________ _____ ______ ______.
___ _________ __________ ___ __________ ___ _________.
____ _______ _______ ___ ______ ________ ____ ______ ______ _______ _________.
________ _______ _______ _________ ________ ___ ___.
__________ ____ _______ ___ _______ ______ ___ ___ _____ ______ _________ ________.
____ _____ ___ ___ ________ ___.
___ ______ ________ _________ ____ __________ ____ ____.
________ _________ ______ __________ __________ _______ _______ _________ _____ ______ ____ _________.
___ _____ _________ ____ ____ __________ ___ ______ ____ _______ ____.
______ _________ ______ _________ _____ ________ ____ _________ ___ ___ _______.
_______ ________ _________ ____ ________ ____.
_____ ______ _______ ______ __________ _________ ______ _________ ________ __________ _____.
_______ _____ ______ _______ ____ _________ ____ ____ _____.
_____ ________ ___ __________ ______ ________ __________ ____ _________ _______.
____ ______ ______ _______ _______ ______ ____.
________ __________ _________ __________ _____ _________ _________ ______ _________.
_________ _______ __________ ________ ____.
__________ ________ _________ __________ _______ _____ _______ _________ _______.
_________ __________ _________ _________ _____.
_____ ______ _________ _____ _________ ____ _____ _______.
________ _______ ______ _____ _________ _______ ___ _________ _________ _______ ______ _______.
_____ _______ ___ ________ ________ __________ ___ ______.
_____ ____ _______ _______ _____.
___ ___ _______ ________ ____ ________ ______ _________ _______.
___ _________ ______ _________ _____ ____ _________ ___.
_______ _________ ________ ________ _________ _____ __________ ________ ______ ____.
__________ ______ ________ _____ _________ _________ _____ _________ ______ ___ ________ _________.
_________ ______ ______.
Get Full Answer on WhatsApp

IGNOU Solved Assignments Assignments Ignou Projects Project Previous Year Solved Exam Papers Notes Notes Sample Question Papers Sample Question Papers

IGNOU NEWS

Assignment Submission Last Date Extended Till 30 June 2026 Click Here★★★IGNOU June 2026 TEE Date Sheet Released Click Here★★★

Sample No.	Obs. 1	Obs. 2	Obs. 3	Obs. 4	Obs. 5	Obs. 6	Obs. 7	Obs. 8	Obs. 9	Obs. 10
1	99.46	100.12	99.73	99.56	99.46	99.73	99.46	100.12	99.73	99.56
2	100.95	100.00	99.66	100.06	100.95	99.66	100.95	100.00	99.66	100.06
3	99.84	99.43	99.62	99.73	99.84	99.62	99.84	99.43	99.62	99.93
4	99.85	99.26	99.77	99.56	99.85	99.77	99.85	99.86	99.77	99.76
5	99.66	100.12	99.91	100.02	99.66	99.91	99.66	100.12	99.91	100.02
6	99.82	100.06	99.87	100.18	99.82	99.87	99.82	100.06	99.87	100.18
7	99.86	99.66	99.46	99.52	99.86	99.46	99.86	99.66	99.86	99.72
8	99.87	99.62	100.12	99.62	99.87	100.12	99.87	99.62	100.12	99.62
9	99.85	99.67	100.13	100.07	99.85	100.13	99.85	99.67	100.13	100.07
10	99.72	99.52	99.85	99.71	99.72	99.85	99.72	99.52	99.85	99.71
11	99.88	100.00	100.26	99.87	99.88	100.26	99.88	100.00	99.86	99.87
12	99.65	100.06	100.15	99.93	99.65	100.15	99.65	100.06	100.15	99.93
13	99.46	99.70	99.43	99.87	99.86	99.63	99.66	99.70	99.83	99.87
14	99.91	99.60	99.75	100.22	99.91	99.75	99.91	99.60	99.75	100.22
15	100.04	100.06	99.82	99.85	100.04	99.82	100.04	100.06	99.82	99.85
16	100.15	100.10	99.93	99.62	100.15	99.93	100.15	100.10	99.93	99.62
17	100.13	99.56	98.81	99.25	100.13	98.81	100.13	99.56	98.81	99.25
18	99.82	100.05	100.08	99.75	99.82	100.08	99.82	100.05	100.08	99.75
19	99.90	100.10	99.91	100.15	99.90	99.91	99.90	100.10	99.91	100.15
20	99.50	99.76	99.95	99.56	99.50	99.95	99.50	99.76	99.95	99.56
21	99.88	100.12	100.00	100.25	99.88	100.00	99.88	99.92	100.00	100.05
22	99.87	99.67	99.51	99.71	99.87	99.51	99.87	99.67	99.51	99.71
23	100.31	99.91	99.60	99.96	100.31	99.60	100.31	99.91	99.60	99.96
24	99.66	99.46	99.91	99.72	99.66	99.91	99.66	99.46	99.91	99.72
25	99.90	100.02	99.70	100.07	99.90	99.70	99.90	100.02	99.70	100.07

City	Number of Weekly Commuters	Average Petrol Price	Population of City (in ’000)	Average Monthly Income of Commuters (in ’00)	Average Monthly Parking Rates (in ₹)
1	17700	75	1900	580	1000
2	17540	75	1890	620	1000
3	17620	75	1880	640	1200
4	16260	77	1878	650	1200
5	16180	77	1850	655	1200
6	16340	77	1840	658	1400
7	16580	77	1825	820	1500
8	16020	82	1825	860	1500
9	15940	82	1820	880	1500
10	15892	82	1805	920	1600
11	15780	85	1810	963	1600
12	14820	95	1800	1057	1600
13	14660	95	1795	1133	1700
14	14660	96	1795	1160	2000
15	14580	96	1790	1180	2100
16	14420	96	1730	1183	2100
17	13380	97	1740	1265	2100
18	10070	120	1735	1300	2200
19	13220	102	1730	1325	2500
20	13540	102	1720	1380	2600
21	13700	102	1715	1401	3000
22	12100	107	1705	1450	3100
23	11124	113	1690	1500	3300
24	10900	125	1695	1520	3500
25	11108	114	1690	1560	3500
26	13668	104	1700	1600	3800
27	13780	90	1710	1620	4000
28	12108	118	1790	1590	3700
29	14668	108	1800	1630	4000
30	14780	94	1810	1650	4200

Days	Total Inspected Cars	Number of Defects
1	45	6
2	35	2
3	40	1
4	30	2
5	40	5
6	25	1
7	35	3
8	30	4
9	30	6
10	40	2
11	35	11
12	35	1
13	25	3
14	40	7
15	45	2
16	40	6
17	30	5
18	35	2
19	30	7
20	45	3
21	28	1
22	38	4
23	33	11
24	33	1
25	43	4
26	38	2
27	38	5
28	28	4
29	43	6
30	48	1
31	43	3
32	33	4
33	38	3
34	33	2
35	48	5