Regression Model
y = a0 + a1 x1 + a2 x2 + a3 x3 + a4 x4
where y and xi map to:
HardHeat = a0 + a1 Wpc1 + a2 Wpc2 + a3 Wpc3 + a4 Wpc4
| Variable | Value | 95% confidence |
|---|---|---|
| a0 | 60.898935 | 161.617 |
| a1 | 1.5627294 | 1.71780 |
| a2 | 0.52650280 | 1.66940 |
| a3 | 0.11254519 | 1.74072 |
| a4 | -0.12661813 | 1.63541 |
| R² | R²adj | Rmsd | Variance |
|---|---|---|---|
| 0.982324 | 0.973487 | 0.532292 | 5.98544 |
Multilinear Regression Fit
Multilinear Regression HardHeat Residuals
Data Table
| Wpc1 | Wpc2 | Wpc3 | Wpc4 | HardHeat | Calculated HardHeat | Residual % | |
|---|---|---|---|---|---|---|---|
| 1 | 7 | 26 | 6 | 60 | 78.7 | 78.605297 | 0.1203% |
| 2 | 1 | 29 | 15 | 52 | 74.3 | 72.834280 | 1.973% |
| 3 | 11 | 56 | 8 | 20 | 104.3 | 105.94111 | -1.573% |
| 4 | 11 | 31 | 8 | 47 | 87.6 | 89.359854 | -2.009% |
| 5 | 7 | 52 | 6 | 33 | 95.9 | 95.713059 | 0.1949% |
| 6 | 11 | 55 | 9 | 22 | 109.2 | 105.27392 | 3.595% |
| 7 | 3 | 71 | 17 | 6 | 102.7 | 104.12238 | -1.385% |
| 8 | 1 | 31 | 22 | 44 | 72.5 | 75.688047 | -4.397% |
| 9 | 2 | 54 | 18 | 22 | 93.1 | 91.695759 | 1.508% |
| 10 | 21 | 47 | 4 | 26 | 115.9 | 115.61999 | 0.2416% |
| 11 | 1 | 40 | 23 | 34 | 83.8 | 81.805299 | 2.380% |
| 12 | 11 | 66 | 9 | 12 | 113.3 | 112.33163 | 0.8547% |
| 13 | 10 | 68 | 8 | 12 | 109.4 | 111.70936 | 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 |
Source
# 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 [...] [origin]
mlinfit Wpc1 Wpc2 Wpc3 Wpc4 HardHeat
# 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
mlinfit Wpc1 Wpc2 Wpc3 Wpc4 HardHeat