# Example 31(a) - Multi-Linear Regression
# Heat of Hardening
# Verified Solution: a0=60.8989, a1=1.56273, a2=0.526503, a3=0.112545 , a4=-0.126618
# 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 <x1> <x2> <x3> [...] <y> [origin]
mlinfit Wpc1 Wpc2 Wpc3 Wpc4 HardHeat
HardHeat = a0 + a1Wpc1 + a2Wpc2 + a3Wpc3 + a4Wpc4
| Variable |
Value |
95% confidence |
| a0 |
60.898935 |
161.61721 |
| a1 |
1.5627294 |
1.7177962 |
| a2 |
0.5265028 |
1.6694019 |
| a3 |
0.11254519 |
1.7407207 |
| a4 |
-0.12661813 |
1.6354138 |
| R^2 |
R^2adj |
Rmsd |
Variance |
| 0.9823245 |
0.9734867 |
0.5322918 |
5.985442 |
Regression 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 |
78.605297 |
0.09470346 |
| 2 |
1 |
29 |
15 |
52 |
74.3 |
72.83428 |
1.4657198 |
| 3 |
11 |
56 |
8 |
20 |
104.3 |
105.94111 |
-1.641114 |
| 4 |
11 |
31 |
8 |
47 |
87.6 |
89.359854 |
-1.7598543 |
| 5 |
7 |
52 |
6 |
33 |
95.9 |
95.713059 |
0.186941 |
| 6 |
11 |
55 |
9 |
22 |
109.2 |
105.27392 |
3.9260799 |
| 7 |
3 |
71 |
17 |
6 |
102.7 |
104.12238 |
-1.4223813 |
| 8 |
1 |
31 |
22 |
44 |
72.5 |
75.688047 |
-3.1880472 |
| 9 |
2 |
54 |
18 |
22 |
93.1 |
91.695759 |
1.4042407 |
| 10 |
21 |
47 |
4 |
26 |
115.9 |
115.61999 |
0.28000661 |
| 11 |
1 |
40 |
23 |
34 |
83.8 |
81.805299 |
1.994701 |
| 12 |
11 |
66 |
9 |
12 |
113.3 |
112.33163 |
0.96836772 |
| 13 |
10 |
68 |
8 |
12 |
109.4 |
111.70936 |
-2.3093633 |
General
Number of independent variables = 4
Regression including a free parameter
Number of observations = 13