Más contenido relacionado La actualidad más candente (20) Similar a Mpc 006 - 02-03 partial and multiple correlation (20) Más de Vasant Kothari (20) Mpc 006 - 02-03 partial and multiple correlation9. 𝑟 𝑝 = 𝑟 𝐴𝐵. 𝐶 =
𝑟𝐴𝐵 − 𝑟𝐴𝐶 𝑟𝐵𝐶
1 − 𝑟𝐴𝐶
2
1 − 𝑟𝐵𝐶
2
11. 𝑟 𝐴𝐵 = −0.369 𝑟 𝐴𝐶 = 0.918
𝑟 𝐵𝐶 = −0.245
12. 𝑟 𝑝 = 𝑟 𝐴𝐵. 𝐶 =
(−0.369) − (0.918)(−0.245)
1 − 0.9182
1 − −0.245 2
𝑟 𝑝 = 𝑟 𝐴𝐵. 𝐶 =
−0.1441
0.499
𝑟 𝑝 = 𝑟 𝐴𝐵. 𝐶 = −0.375
18. 𝑯 𝟎 = 𝝆 𝑨𝑩. 𝑪
𝒂𝒈𝒂𝒊𝒏𝒔𝒕
𝑯 𝟏 ≠ 𝝆 𝑨𝑩. 𝑪
20. 𝒕 =
𝒓 𝒑 𝒏 − 𝒗
𝟏 − 𝒓 𝒑
𝟐
rp = partial correlation computed on sample, rAB.C
n = sample size,
v = total number of variables employed in the analysis
22. 𝒕 =
𝒓 𝒑 𝒏 − 𝒗
𝟏 − 𝒓 𝒑
𝟐
𝒕 =
−𝟎. 𝟑𝟕𝟓 𝟏𝟎 − 𝟑
𝟏 − −𝟎. 𝟑𝟕𝟓 𝟐
=
−𝟎. 𝟗𝟗𝟐
𝟎. 𝟗𝟐𝟕
= 𝟏. 𝟔𝟗
23. df/
α (2 tail)
0.1 0.05 0.02 0.01
1 6.3138 12.7065 31.8193 63.6551
2 2.9200 4.3026 6.9646 9.9247
3 2.3534 3.1824 4.5407 5.8408
4 2.1319 2.7764 3.7470 4.6041
5 2.0150 2.5706 3.3650 4.0322
6 1.9432 2.4469 3.1426 3.7074
7 1.8946 2.3646 2.9980 3.4995
8 1.8595 2.3060 2.8965 3.3554
9 1.8331 2.2621 2.8214 3.2498
10 1.8124 2.2282 2.7638 3.1693
37. 𝒚𝒊 = 𝜷 𝟎 + 𝜷 𝟏 𝒙𝒊+∈𝒊
X
Y
xi
𝑆𝑙𝑜𝑝𝑒 = 𝛽1
𝐼𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡
= 𝛽0
𝑂𝑏𝑠𝑒𝑟𝑣𝑒𝑑 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓
𝑌 𝑓𝑜𝑟 𝑋𝑖
𝑃𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓
𝑌 𝑓𝑜𝑟 𝑋𝑖
∈𝑖
𝑅𝑎𝑛𝑑𝑜𝑚 𝐸𝑟𝑟𝑜𝑟
𝑓𝑜𝑟 𝑡ℎ𝑖𝑠 𝑋𝑖 𝑣𝑎𝑙𝑢𝑒
38. 𝛽1 =
𝑥 − 𝑥 𝑦 − 𝑦
𝑥 − 𝑥 2 =
𝑥𝑦 − 𝑛 𝑥 𝑦
𝑥2 − 𝑛 𝑥2
=
𝑥𝑦 −
𝑥 𝑦
𝑛
𝑥2 −
𝑥 2
𝑛
𝛽1 =
𝑆𝑆 𝑥𝑦
𝑆𝑆 𝑥𝑥
𝛽0 = 𝑦 − 𝛽1 𝑥 =
𝑦
𝑛
− 𝛽1
𝑥
𝑛
39. x y x2 xy
1 4 1 4
3 2 9 6
4 1 16 4
5 0 25 0
8 0 64 0
21 7 115 14
40. 𝛽1 =
𝑥𝑦 −
𝑥 𝑦
𝑛
𝑥2 −
𝑥 2
𝑛
=
14 −
21 ∗ 7
5
115 −
21 2
5
=
−15.4
26.8
= −0.575
𝛽0 =
𝑦
𝑛
− 𝛽1
𝑥
𝑛
=
7
5
− −0.575
21
7
= 3.81
𝒚 = 𝟑. 𝟖𝟏 − 𝟎. 𝟓𝟕𝟓𝒙
44. ∈ 𝟏 ∈ 𝟐
𝑟 𝑝 = ∈ 𝟏 ∈ 𝟐
48. 𝒂 + 𝒃 + 𝒄 + 𝒅 = 𝒗𝒂𝒓𝒊𝒂𝒏𝒄𝒆 𝒊𝒏 𝑫𝑽
𝒂 + 𝒃 + 𝒄 = 𝒗𝒂𝒓𝒊𝒂𝒏𝒄𝒆 𝒊𝒏 𝑫𝑽
𝒆𝒙𝒑𝒍𝒂𝒊𝒏𝒆𝒅 𝒃𝒚 𝑰𝑽 𝟏 &𝑰𝑽 𝟐
𝒂 + 𝒄 = 𝒖𝒏𝒊𝒒𝒖𝒆𝒍𝒚 𝒆𝒙𝒑𝒍𝒂𝒊𝒏𝒆𝒅
𝒗𝒂𝒓𝒊𝒂𝒏𝒄𝒆
𝒃 = 𝒏𝒐𝒏 − 𝒖𝒏𝒊𝒒𝒖𝒆𝒍𝒚 𝒆𝒙𝒑𝒍𝒂𝒊𝒏𝒆𝒅
𝒗𝒂𝒓𝒊𝒂𝒏𝒄𝒆
57. 𝒓 𝑺𝑷 = 𝒓 𝑩 𝑨.𝑪 =
𝒓 𝑨𝑩 − 𝒓 𝑨𝑪 𝒓 𝑩𝑪
𝟏 − 𝒓 𝑨𝑪
𝟐
59. 𝑟 𝐴𝐵 = −0.369 𝑟 𝐴𝐶 = 0.918
𝑟 𝐵𝐶 = −0.245
60. 𝑟 𝑆𝑃 = 𝑟 𝐵( 𝐴. 𝐶)
=
(−0.369) − (0.918)(−0.245)
1 − 0.9182
𝑟 𝑆𝑃 = 𝑟 𝐵( 𝐴. 𝐶)
=
−0.1441
0.3966
𝑟 𝑆𝑃 = 𝑟 𝐵( 𝐴. 𝐶)
= −0.363
64. 𝑯 𝟎: 𝝆 𝑺𝑷 = 𝟎
𝒂𝒈𝒂𝒊𝒏𝒔𝒕
𝑯 𝟏: 𝝆 𝑺𝑷 ≠ 𝟎
66. 𝒕 =
𝒓 𝒔𝒑 𝒏 − 𝒗
𝟏 − 𝒓 𝒔𝒑
𝟐
rp = semi-partial correlation computed on sample, rB(A.C)
n = sample size,
v = total number of variables employed in the analysis
68. 𝒕 =
𝒓 𝒔𝒑 𝒏 − 𝒗
𝟏 − 𝒓 𝒔𝒑
𝟐
𝒕 =
−𝟎. 𝟑𝟔𝟑 𝟏𝟎 − 𝟑
𝟏 − −𝟎. 𝟑𝟔𝟑 𝟐
= −𝟏. 𝟎𝟑𝟐
69. df/
α (2 tail)
0.1 0.05 0.02 0.01
1 6.3138 12.7065 31.8193 63.6551
2 2.9200 4.3026 6.9646 9.9247
3 2.3534 3.1824 4.5407 5.8408
4 2.1319 2.7764 3.7470 4.6041
5 2.0150 2.5706 3.3650 4.0322
6 1.9432 2.4469 3.1426 3.7074
7 1.8946 2.3646 2.9980 3.4995
8 1.8595 2.3060 2.8965 3.3554
9 1.8331 2.2621 2.8214 3.2498
10 1.8124 2.2282 2.7638 3.1693
80. 𝑹 𝑨.𝑩𝑪 =
𝒓 𝑨𝑩
𝟐
+ 𝒓 𝑨𝑪
𝟐
− 𝟐𝒓 𝑨𝑩 𝒓 𝑨𝑪 𝒓 𝑩𝑪
𝟏 − 𝒓 𝑩𝑪
𝟐
R A . BC = is multiple correlation between A & linear combination of B and C
rAB = is correlation between A and B
rAC = is correlation between A and C
rBC = is correlation between B and C
82. 𝑟 𝐴𝐵 = −0.369 𝑟 𝐴𝐶 = 0.918
𝑟 𝐵𝐶 = −0.245
83. 𝑅 𝐴. 𝐵𝐶 =
−0.369 2 + 0.918 2 −2 −.369 .918 −.245
1 − −0.245 2
𝑅 𝐴. 𝐵𝐶 =
0.813
0.94
𝑅 𝐴. 𝐵𝐶 = 0.929
87. R = 0 R2 = 0
Variance = 0%
R = ±0.2 R2 = 0.04
Variance = 4%
R = ±0.4 R2 = 0.16
Variance = 16%
88. R = ±0.6 R2 = 0.36
Variance = 36%
R = ±0.8 R2 = 0.64
Variance = 64%
R = ±1 R2 = 1
Variance = 100%
91. 𝑹 𝟐 = 𝟏 −
𝟏 − 𝑹 𝟐
𝒏 − 𝟏
𝒏 − 𝒌 − 𝟏
𝑅2 = is adjusted value of R2
k = number of predicted variables
n = sample size
92. 𝑹 𝟐 = 𝟏 −
𝟏 − 𝑹 𝟐
𝒏 − 𝟏
𝒏 − 𝒌 − 𝟏
= 𝟏 −
𝟏 − 𝟎. 𝟖𝟔𝟓 𝟏𝟎 − 𝟏
𝟏𝟎 − 𝟐 − 𝟏
= 𝟏 −
𝟏. 𝟐𝟏𝟕
𝟕
= 𝟎. 𝟖𝟐𝟔
96. 𝑯 𝟎: 𝝆 𝟐 = 𝟎
𝒂𝒈𝒂𝒊𝒏𝒔𝒕
𝑯 𝟏: 𝝆 𝟐 ≠ 𝟎
100. 𝑭 =
𝟏𝟎 − 𝟐 − 𝟏 𝟎. 𝟖𝟐𝟔
𝟐(𝟏 − 𝟎. 𝟖𝟐𝟔)
𝑭 =
𝒏 − 𝒌 − 𝟏 𝑹 𝟐
𝒌 𝟏 − 𝑹 𝟐
𝑭 =
𝟓. 𝟕𝟖𝟑
𝟎. 𝟑𝟒𝟖
𝑭 = 𝟏𝟔. 𝟔𝟑𝟓
101. 𝑑𝑓1 = 𝑘 = 2 𝑑𝑓2 = 10 − 2 − 1 = 7 𝛼 = 5%
𝐹2,7
𝐶𝑉
= 4.74