# Example 31(b) - Multi-Linear Regression via origin
# Heat of Hardening
# Verified Solution: a1=2.18918, a2=1.15414, a3=0.753295 , a4=0.488545
# Ref: Comput Appl Eng Educ 17: 285, 1998
[
Wpc1 Wpc2 Wpc3 Wpc4 HardHeat
7 26 6 60 78.7
1 29 15 52 74.3
11 56 8 20 104.3
11 31 8 47 87.6
7 52 6 33 95.9
11 55 9 22 109.2
3 71 17 6 102.7
1 31 22 44 72.5
2 54 18 22 93.1
21 47 4 26 115.9
1 40 23 34 83.8
11 66 9 12 113.3
10 68 8 12 109.4
]
mlinfit Wpc1 Wpc2 Wpc3 Wpc4 HardHeat origin
HardHeat = a1Wpc1 + a2Wpc2 + a3Wpc3 + a4Wpc4
| Variable |
Value |
95% confidence |
| a1 |
2.1891766 |
0.41826867 |
| a2 |
1.1541357 |
0.10823254 |
| a3 |
0.75329494 |
0.36011122 |
| a4 |
0.48854515 |
0.09348302 |
| R^2 |
R^2adj |
Rmsd |
Variance |
| 0.9806563 |
0.9742084 |
0.5568439 |
5.822523 |
Multiple Linear Regression via Origin Plot

Residuals Plot

Source data points and calculated data points
| |
Wpc1 |
Wpc2 |
Wpc3 |
Wpc4 |
HardHeat |
HardHeat calc |
Delta HardHeat |
| 1 |
7 |
26 |
6 |
60 |
78.7 |
79.164242 |
-0.46424225 |
| 2 |
1 |
29 |
15 |
52 |
74.3 |
72.362883 |
1.9371171 |
| 3 |
11 |
56 |
8 |
20 |
104.3 |
104.5098 |
-0.20980244 |
| 4 |
11 |
31 |
8 |
47 |
87.6 |
88.84713 |
-1.2471299 |
| 5 |
7 |
52 |
6 |
33 |
95.9 |
95.98105 |
-0.0810505 |
| 6 |
11 |
55 |
9 |
22 |
109.2 |
105.08605 |
4.113948 |
| 7 |
3 |
71 |
17 |
6 |
102.7 |
104.24845 |
-1.548447 |
| 8 |
1 |
31 |
22 |
44 |
72.5 |
76.035858 |
-3.5358576 |
| 9 |
2 |
54 |
18 |
22 |
93.1 |
91.008981 |
2.0910185 |
| 10 |
21 |
47 |
4 |
26 |
115.9 |
115.93244 |
-0.03243851 |
| 11 |
1 |
40 |
23 |
34 |
83.8 |
82.290922 |
1.5090779 |
| 12 |
11 |
66 |
9 |
12 |
113.3 |
112.89609 |
0.40390716 |
| 13 |
10 |
68 |
8 |
12 |
109.4 |
112.26189 |
-2.8618926 |
General
Number of independent variables = 4
Regression not including a free parameter
Number of observations = 13