Regression Model
y = a0 x1 + a1 x2 + a2 x3 + a3 x4
where y and xi map to:
HardHeat = a0 Wpc1 + a1 Wpc2 + a2 Wpc3 + a3 Wpc4
| Variable | Value | 95% confidence |
|---|---|---|
| a0 | 2.1891766 | 0.418269 |
| a1 | 1.1541357 | 0.108233 |
| a2 | 0.75329494 | 0.360111 |
| a3 | 0.48854515 | 0.0934830 |
| R² | R²adj | Rmsd | Variance |
|---|---|---|---|
| 0.980656 | 0.974208 | 0.556844 | 5.82252 |
Multilinear Regression Fit
Multilinear Regression HardHeat Residuals
Data Table
| Wpc1 | Wpc2 | Wpc3 | Wpc4 | HardHeat | Calculated HardHeat | Residual % | |
|---|---|---|---|---|---|---|---|
| 1 | 7 | 26 | 6 | 60 | 78.7 | 79.164242 | -0.5899% |
| 2 | 1 | 29 | 15 | 52 | 74.3 | 72.362883 | 2.607% |
| 3 | 11 | 56 | 8 | 20 | 104.3 | 104.50980 | -0.2012% |
| 4 | 11 | 31 | 8 | 47 | 87.6 | 88.847130 | -1.424% |
| 5 | 7 | 52 | 6 | 33 | 95.9 | 95.981050 | -0.08452% |
| 6 | 11 | 55 | 9 | 22 | 109.2 | 105.08605 | 3.767% |
| 7 | 3 | 71 | 17 | 6 | 102.7 | 104.24845 | -1.508% |
| 8 | 1 | 31 | 22 | 44 | 72.5 | 76.035858 | -4.877% |
| 9 | 2 | 54 | 18 | 22 | 93.1 | 91.008981 | 2.246% |
| 10 | 21 | 47 | 4 | 26 | 115.9 | 115.93244 | -0.02799% |
| 11 | 1 | 40 | 23 | 34 | 83.8 | 82.290922 | 1.801% |
| 12 | 11 | 66 | 9 | 12 | 113.3 | 112.89609 | 0.3565% |
| 13 | 10 | 68 | 8 | 12 | 109.4 | 112.26189 | 0.000% |
Settings and Hints
| Name/Source | Value | Type | |
|---|---|---|---|
| 1 | Independent variables | 4 | Setting |
| 2 | Sample data | 13 | Setting |
| 3 | Version | 7.0.73 | Setting |
| 4 | #@report_fix_digits = 8 | Default (integer) | |
| 5 | #@chart_size = 428,300 | Default (array) | |
| 6 | #@report_show_source = true | Default (boolean) | |
| 7 | #@report_show_header = false | Default (boolean) | |
| 8 | #@report_show_settings = true | Default (boolean) | |
| 9 | #@report_show_charts = true | Default (boolean) | |
| 10 | #@report_show_data_points = true | Default (boolean) | |
Messages
| Severity | Description | |
|---|---|---|
| 1 | Info | -Infor- 5 Known vectors variables (Wpc1, Wpc2, Wpc3, Wpc4, HardHeat) |
| 2 | Info | -Infor- 0 Explicit expressions |
| 3 | Info | -Infor- Regression command: mlinfit Wpc1 Wpc2 Wpc3 Wpc4 HardHeat origin |
Source
# 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
# 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