Correlation Coefficient
nΣ xy - Σ xΣ y
r=
[nΣ x2 - (Σ x)2][nΣ y2 - (Σ y)2]
© 2008 Prentice Hall, Inc. 4 – 100
y
Correlation Coefficient y
nΣ xy - Σ xΣ y
r=
[
(a) Perfect positivenΣx x 2
- ( Σ x )2
][n Σ y Σ
(b) Positive ]
2
- ( y ) 2
x
correlation: correlation:
r = +1 0<r<1
y y
(c) No correlation: x (d) Perfect negative x
r=0 correlation:
r = -1
© 2008 Prentice Hall, Inc. 4 – 101
Year (X) Demand (YA) YF Error 160
2006 90 121.375 31.375 150
2007 100 116.66875 16.66875 140
130
2008 108 114.1684375 6.1684375
Demand
120
2009 115 113.2431719 1.7568281 110
2010 123 113.5066961 9.4933039 100
2011 136 114.9306917 21.069308 90
80
2012 144 118.0910879 25.908912 2006 2007 2008 2009 2010 2011 2012 2013 2014
Year
2013 155 121.9774247 33.022575
2014 126.930811
MAD
Average 121.375 18.182889
Month (X) Sales (y) XY X^2 YF Error
650
1 430 430 1 427.96 2.04
600
2 446 892 4 445.59 0.41
550
3 464 1392 9 463.22 0.78
Sales
4 480 1920 16 480.85 0.85 500
5 498 2490 25 498.48 0.48 450
6 514 3084 36 516.11 2.11 400
0 2 4 6 8 10 12
7 532 3724 49 533.74 1.74 Month
8 548 4384 64 551.37 3.37
9 570 5130 81 569 1
10 591 5910 100 586.63 4.37 a=410.33 Y(X=11)
Sum MAD b=17.63 604.26
55 5073 29356 385 1.715 r=0.999
X Y XY X^2 YF Error 15
162 12 1944 144 11.69 0.314 Number of Needed Wing Flaps
14
149 9 1341 81 10.48 1.477 13
185 13 2405 169 13.83 0.825 12
11
171 14 2394 196 12.52 1.477
10
138 10 1380 100 9.454 0.546
9
154 11 1694 121 10.94 0.058
8
Sum MAD 140 145 150 155 160 165 170 175 180 185 190
Flying Hours (1,000s)
959 69 11158 811 0.783
a=-3.38 Y(X=150,000)
b=0.093 10.57
r=0.83
X Y XY X^2 YF Error 24
225 16 3600 50625 15.685 0.315 23
Sales (Thousands of Passengers)
22
400 21 8400 160000 21.11 0.11 21
350 20 7000 122500 19.56 0.44 20
19
275 17 4675 75625 17.235 0.235 18
450 23 10350 202500 22.66 0.34 17
16
Sum MAD 15
1700 97 34025 611250 0.288 200 250 300 350
Amount of Advertising ($1,000s)
400 450 500
a=8.71 Y(X=300,000)
b=0.031 18.01
r=0.994
Average Periodic Average Weekely Sesonal
Week 1 Week 2 Week 3 Week 4 100
Demand demand Index
95
17.8 18.145 0.98099
Total Demand
Monday 16.2 17.3 18.6 19.1
90
Tuesday 12.2 13.5 14.1 15.8 13.9 18.145 0.76605
85
Wednesday 14.2 15 16 17.9 15.775 18.145 0.86939
80
Thursday 17.3 18.6 19.9 20.6 19.1 18.145 1.05263 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Week
Friday 22.5 23.9 24.9 25.3 24.15 18.145 1.33095
Sum Sum
82.4 88.3 93.5 98.7 90.725
X Y XY X^2 YF Error Week 5
1 82.4 82.4 1 82.61 0.21 a=77.2 Y (X=5) Monday 20.45356848
2 88.3 176.6 4 88.02 0.28 b=5.41 104.25 Tuesday 15.97216864
3 98.7 296.1 9 93.43 5.27 r=0.999 Wednesday 18.12668779
4 90.725 362.9 16 98.84 8.115 Thursday 21.94736842
Sum MAD Friday 27.75020667
360.13 918 30 362.9 3.46875
Find the forecasted demand for each of the four quarters of year 6
Year Q1 Q2 Q3 Q4
1 190 370 300 220
2 280 420 310 180
3 270 360 280 190
4 300 430 290 200
5 320 440 320 220
6 ? ? ? ?
Solution
Year Q YA 4 Period MA Centered MA SI = YA/C.M.A Q1 Q2 Q3 Q4
Q1 190 Year 1 1.07 0.74
Year 2 0.91 1.39 1.05 0.63
Q2 370 Year 3 0.98 1.32 1.00 0.65
Year 1
270 Year 4 0.99 1.41 0.94 0.64
Q3 300 281.25 1.07 Year 5 1.01 1.36
292.5
Q4 220 298.75 0.74 Average 0.97 1.37 1.02 0.66
305
Q1 280 306.25 0.91 Year 6 308.19 441.95 312.16 206.78
307.5
Q2 420 302.5 1.39
Year 2
297.5
Q3 310 296.25 1.05
295
Q4 180 287.5 0.63
280
Q1 270 276.25 0.98
272.5
Q2 360 273.75 1.32
Year 3
275
Q3 280 278.75 1.00
282.5
Q4 190 291.25 0.65
300
Q1 300 301.67 0.99
303.33
Q2 430 304.17 1.41
Year 4
305
Q3 290 307.5 0.94
310
Q4 200 311.25 0.64
312.5
Q1 320 316.25 1.01
320
Q2 440 322.5 1.36
Year 5
325
Q3 320
Q4 220
