| EXST7034 - Bodyfat Example, KNNL Table 7.1 |
| Raw Data Listing |
| Obs | Y | X1 | X2 | X3 |
|---|---|---|---|---|
| 1 | 12.8 | 14.6 | 42.7 | 21.3 |
| 2 | 11.7 | 18.7 | 46.5 | 23.0 |
| 3 | 12.9 | 19.1 | 42.2 | 30.9 |
| 4 | 11.9 | 19.5 | 43.1 | 29.1 |
| 5 | 17.8 | 19.7 | 44.2 | 28.6 |
| 6 | 21.3 | 22.1 | 49.9 | 23.2 |
| 7 | 14.8 | 22.7 | 48.2 | 27.1 |
| 8 | 22.8 | 24.7 | 49.8 | 28.2 |
| 9 | 21.1 | 25.2 | 51.0 | 27.5 |
| 10 | 19.3 | 25.5 | 53.5 | 24.8 |
| 11 | 21.7 | 25.6 | 53.9 | 23.7 |
| 12 | 22.6 | 27.7 | 55.3 | 25.7 |
| 13 | 25.4 | 27.9 | 52.1 | 30.6 |
| 14 | 23.9 | 29.5 | 54.4 | 30.1 |
| 15 | 20.1 | 29.8 | 54.3 | 31.1 |
| 16 | 25.4 | 30.2 | 58.6 | 24.6 |
| 17 | 27.2 | 30.4 | 56.7 | 28.3 |
| 18 | 18.7 | 30.7 | 51.9 | 37.0 |
| 19 | 25.4 | 31.1 | 56.6 | 30.0 |
| 20 | 27.1 | 31.4 | 58.5 | 27.6 |
| EXST7034 - Bodyfat Example, KNNL Table 7.1 |
| Simple Linear fits : Body Fat |
| Number of Observations Read | 20 |
|---|---|
| Number of Observations Used | 20 |
| Analysis of Variance | |||||
|---|---|---|---|---|---|
| Source | DF | Sum of Squares |
Mean Square |
F Value | Pr > F |
| Model | 1 | 352.26980 | 352.26980 | 44.30 | <.0001 |
| Error | 18 | 143.11970 | 7.95109 | ||
| Corrected Total | 19 | 495.38950 | |||
| Root MSE | 2.81977 | R-Square | 0.7111 |
|---|---|---|---|
| Dependent Mean | 20.19500 | Adj R-Sq | 0.6950 |
| Coeff Var | 13.96271 |
| Parameter Estimates | |||||
|---|---|---|---|---|---|
| Variable | DF | Parameter Estimate |
Standard Error |
t Value | Pr > |t| |
| Intercept | 1 | -1.49610 | 3.31923 | -0.45 | 0.6576 |
| X1 | 1 | 0.85719 | 0.12878 | 6.66 | <.0001 |
| EXST7034 - Bodyfat Example, KNNL Table 7.1 |
| Simple Linear fits : Body Fat |
| Number of Observations Read | 20 |
|---|---|
| Number of Observations Used | 20 |
| Analysis of Variance | |||||
|---|---|---|---|---|---|
| Source | DF | Sum of Squares |
Mean Square |
F Value | Pr > F |
| Model | 1 | 381.96582 | 381.96582 | 60.62 | <.0001 |
| Error | 18 | 113.42368 | 6.30132 | ||
| Corrected Total | 19 | 495.38950 | |||
| Root MSE | 2.51024 | R-Square | 0.7710 |
|---|---|---|---|
| Dependent Mean | 20.19500 | Adj R-Sq | 0.7583 |
| Coeff Var | 12.43002 |
| Parameter Estimates | |||||
|---|---|---|---|---|---|
| Variable | DF | Parameter Estimate |
Standard Error |
t Value | Pr > |t| |
| Intercept | 1 | -23.63449 | 5.65741 | -4.18 | 0.0006 |
| X2 | 1 | 0.85655 | 0.11002 | 7.79 | <.0001 |
| EXST7034 - Bodyfat Example, KNNL Table 7.1 |
| Simple Linear fits : Body Fat |
| Number of Observations Read | 20 |
|---|---|
| Number of Observations Used | 20 |
| Analysis of Variance | |||||
|---|---|---|---|---|---|
| Source | DF | Sum of Squares |
Mean Square |
F Value | Pr > F |
| Model | 1 | 10.05160 | 10.05160 | 0.37 | 0.5491 |
| Error | 18 | 485.33790 | 26.96322 | ||
| Corrected Total | 19 | 495.38950 | |||
| Root MSE | 5.19261 | R-Square | 0.0203 |
|---|---|---|---|
| Dependent Mean | 20.19500 | Adj R-Sq | -0.0341 |
| Coeff Var | 25.71236 |
| Parameter Estimates | |||||
|---|---|---|---|---|---|
| Variable | DF | Parameter Estimate |
Standard Error |
t Value | Pr > |t| |
| Intercept | 1 | 14.68678 | 9.09593 | 1.61 | 0.1238 |
| X3 | 1 | 0.19943 | 0.32663 | 0.61 | 0.5491 |
| EXST7034 - Bodyfat Example, KNNL Table 7.1 |
| Multiple regression : Body Fat |
| Number of Observations Read | 20 |
|---|---|
| Number of Observations Used | 20 |
| Analysis of Variance | |||||
|---|---|---|---|---|---|
| Source | DF | Sum of Squares |
Mean Square |
F Value | Pr > F |
| Model | 3 | 396.98461 | 132.32820 | 21.52 | <.0001 |
| Error | 16 | 98.40489 | 6.15031 | ||
| Corrected Total | 19 | 495.38950 | |||
| Root MSE | 2.47998 | R-Square | 0.8014 |
|---|---|---|---|
| Dependent Mean | 20.19500 | Adj R-Sq | 0.7641 |
| Coeff Var | 12.28017 |
| Parameter Estimates | ||||||||
|---|---|---|---|---|---|---|---|---|
| Variable | DF | Parameter Estimate |
Standard Error |
t Value | Pr > |t| | Standardized Estimate |
Tolerance | Variance Inflation |
| Intercept | 1 | 117.08469 | 99.78240 | 1.17 | 0.2578 | 0 | . | 0 |
| X1 | 1 | 4.33409 | 3.01551 | 1.44 | 0.1699 | 4.26370 | 0.00141 | 708.84291 |
| X2 | 1 | -2.85685 | 2.58202 | -1.11 | 0.2849 | -2.92870 | 0.00177 | 564.34339 |
| X3 | 1 | -2.18606 | 1.59550 | -1.37 | 0.1896 | -1.56142 | 0.00956 | 104.60601 |
| Sequential Parameter Estimates | |||
|---|---|---|---|
| Intercept | X1 | X2 | X3 |
| 20.195000 | 0 | 0 | 0 |
| -1.496105 | 0.857187 | 0 | 0 |
| -19.174246 | 0.222353 | 0.659422 | 0 |
| 117.084695 | 4.334092 | -2.856848 | -2.186060 |
| Collinearity Diagnostics | ||||||
|---|---|---|---|---|---|---|
| Number | Eigenvalue | Condition Index |
Proportion of Variation | |||
| Intercept | X1 | X2 | X3 | |||
| 1 | 3.96796 | 1.00000 | 0.00000195 | 0.00000320 | 0.00000110 | 0.00000980 |
| 2 | 0.02052 | 13.90482 | 0.00037152 | 0.00132 | 0.00003262 | 0.00139 |
| 3 | 0.01151 | 18.56570 | 0.00059915 | 0.00021875 | 0.00032550 | 0.00693 |
| 4 | 0.00000865 | 677.37207 | 0.99903 | 0.99846 | 0.99964 | 0.99167 |
| EXST7034 - Bodyfat Example, KNNL Table 7.1 |
| Correlation matrix |
| 4 Variables: | Y X1 X2 X3 |
|---|
| Simple Statistics | ||||||
|---|---|---|---|---|---|---|
| Variable | N | Mean | Std Dev | Sum | Minimum | Maximum |
| Y | 20 | 20.19500 | 5.10619 | 403.90000 | 11.70000 | 27.20000 |
| X1 | 20 | 25.30500 | 5.02326 | 506.10000 | 14.60000 | 31.40000 |
| X2 | 20 | 51.17000 | 5.23461 | 1023 | 42.20000 | 58.60000 |
| X3 | 20 | 27.62000 | 3.64715 | 552.40000 | 21.30000 | 37.00000 |
| Pearson Correlation Coefficients, N = 20 Prob > |r| under H0: Rho=0 |
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