Consider the data on new orders for computers and electronic products and the M1
ID: 472572 • Letter: C
Question
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
Explanation / Answer
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