Consider the data on new orders for computers and electronic

Consider the data on new orders for computers and electronic products and the M1 money supply for the years 2011 through 2014.

Year

Month

New Orders for Computers and Electronic Products

M-1 Money Supply

2011

1

19222

1855.6

2011

2

20727

1874.7

2011

3

24893

1892.0

2011

4

19375

1897.8

2011

5

20152

1934.3

2011

6

25075

1947.0

2011

7

18615

2001.5

2011

8

21289

2112.9

2011

9

27014

2126.0

2011

10

22179

2137.4

2011

11

20761

2172.0

2011

12

27818

2168.2

2012

1

19447

2202.3

2012

2

23043

2212.2

2012

3

26734

2228.7

2012

4

21897

2245.3

2012

5

22403

2251.0

2012

6

24942

2262.3

2012

7

19365

2314.6

2012

8

20240

2346.5

2012

9

25478

2383.6

2012

10

20790

2415.5

2012

11

20362

2423.2

2012

12

27841

2457.7

2013

1

17393

2467.6

2013

2

18725

2470.4

2013

3

22919

2474.8

2013

4

19560

2511.0

2013

5

20333

2522.0

2013

6

24619

2517.9

2013

7

18065

2545.6

2013

8

18487

2557.3

2013

9

24877

2578.8

2013

10

20410

2620.2

2013

11

20194

2622.2

2013

12

24955

2654.5

Using the same data, develop a causal model forecast using the M1 Money Supply data as the independent variable.

Year	Month	New Orders for Computers and Electronic Products	M-1 Money Supply
2011	1	19222	1855.6
2011	2	20727	1874.7
2011	3	24893	1892.0
2011	4	19375	1897.8
2011	5	20152	1934.3
2011	6	25075	1947.0
2011	7	18615	2001.5
2011	8	21289	2112.9
2011	9	27014	2126.0
2011	10	22179	2137.4
2011	11	20761	2172.0
2011	12	27818	2168.2
2012	1	19447	2202.3
2012	2	23043	2212.2
2012	3	26734	2228.7
2012	4	21897	2245.3
2012	5	22403	2251.0
2012	6	24942	2262.3
2012	7	19365	2314.6
2012	8	20240	2346.5
2012	9	25478	2383.6
2012	10	20790	2415.5
2012	11	20362	2423.2
2012	12	27841	2457.7
2013	1	17393	2467.6
2013	2	18725	2470.4
2013	3	22919	2474.8
2013	4	19560	2511.0
2013	5	20333	2522.0
2013	6	24619	2517.9
2013	7	18065	2545.6
2013	8	18487	2557.3
2013	9	24877	2578.8
2013	10	20410	2620.2
2013	11	20194	2622.2
2013	12	24955	2654.5

Solution

b = (xy    - nxy)/( (X^2) – n(x^2))

a = y – bx

Here,

y = 21949.97    (average of Y)

x = 2289.01          (average of X)

b = (1807484146.7 - 36*2289.01*21949.97) / (190657818.38 – 36*2289.01^2)

b = -.633

a = 21949.97 - .633*2289.01

a = 20501.026

Thus,

Causal forecast model is

Y = 20501.026 - .633X

Year	Month	New Orders for Computers and Electronic Products (Y)	M-1 Money Supply                       (X)	X^2	Y^2	XY
2011	1	19222	1855.6	3443251.36	369485284	35668343.2
2011	2	20727	1874.7	3514500.09	429608529	38856906.9
2011	3	24893	1892	3579664	619661449	47097556
2011	4	19375	1897.8	3601644.84	375390625	36769875
2011	5	20152	1934.3	3741516.49	406103104	38980013.6
2011	6	25075	1947	3790809	628755625	48821025
2011	7	18615	2001.5	4006002.25	346518225	37257922.5
2011	8	21289	2112.9	4464346.41	453221521	44981528.1
2011	9	27014	2126	4519876	729756196	57431764
2011	10	22179	2137.4	4568478.76	491908041	47405394.6
2011	11	20761	2172	4717584	431019121	45092892
2011	12	27818	2168.2	4701091.24	773841124	60314987.6
2012	1	19447	2202.3	4850125.29	378185809	42828128.1
2012	2	23043	2212.2	4893828.84	530979849	50975724.6
2012	3	26734	2228.7	4967103.69	714706756	59582065.8
2012	4	21897	2245.3	5041372.09	479478609	49165334.1
2012	5	22403	2251	5067001	501894409	50429153
2012	6	24942	2262.3	5118001.29	622103364	56426286.6
2012	7	19365	2314.6	5357373.16	375003225	44822229
2012	8	20240	2346.5	5506062.25	409657600	47493160
2012	9	25478	2383.6	5681548.96	649128484	60729360.8
2012	10	20790	2415.5	5834640.25	432224100	50218245
2012	11	20362	2423.2	5871898.24	414611044	49341198.4
2012	12	27841	2457.7	6040289.29	775121281	68424825.7
2013	1	17393	2467.6	6089049.76	302516449	42918966.8
2013	2	18725	2470.4	6102876.16	350625625	46258240
2013	3	22919	2474.8	6124635.04	525280561	56719941.2
2013	4	19560	2511	6305121	382593600	49115160
2013	5	20333	2522	6360484	413430889	51279826
2013	6	24619	2517.9	6339820.41	606095161	61988180.1
2013	7	18065	2545.6	6480079.36	326344225	45986264
2013	8	18487	2557.3	6539783.29	341769169	47276805.1
2013	9	24877	2578.8	6650209.44	618865129	64152807.6
2013	10	20410	2620.2	6865448.04	416568100	53478282
2013	11	20194	2622.2	6875932.84	407797636	52952706.8
2013	12	24955	2654.5	7046370.25	622752025	66243047.5
	Mean =	21949.97222	2289.016667	190657818.4	17653001943	1807484147
		Average Y	Average X	Sum of X^2	Sum of Y^2	Sum of X*Y
	Causal Equation is as following:
	Y = a + bX