| Multiple Linear Regression - Estimated Regression Equation |
| HIV_Risk[t] = + 13.4324 + 0.215737Homicides[t] + e[t] |
| Multiple Linear Regression - Ordinary Least Squares | |||||
| Variable | Parameter | S.D. | T-STAT H0: parameter = 0 | 2-tail p-value | 1-tail p-value |
| (Intercept) | +13.43 | 2.751 | +4.8820e+00 | 3.83e-05 | 1.915e-05 |
| Homicides | +0.2157 | 0.04587 | +4.7030e+00 | 6.245e-05 | 3.123e-05 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.6643 |
| R-squared | 0.4413 |
| Adjusted R-squared | 0.4214 |
| F-TEST (value) | 22.12 |
| F-TEST (DF numerator) | 1 |
| F-TEST (DF denominator) | 28 |
| p-value | 6.245e-05 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 7.285 |
| Sum Squared Residuals | 1486 |
| Menu of Residual Diagnostics | |
| Description | Link |
| Histogram | Compute |
| Central Tendency | Compute |
| QQ Plot | Compute |
| Kernel Density Plot | Compute |
| Skewness/Kurtosis Test | Compute |
| Skewness-Kurtosis Plot | Compute |
| Harrell-Davis Plot | Compute |
| Bootstrap Plot -- Central Tendency | Compute |
| Blocked Bootstrap Plot -- Central Tendency | Compute |
| (Partial) Autocorrelation Plot | Compute |
| Spectral Analysis | Compute |
| Tukey lambda PPCC Plot | Compute |
| Box-Cox Normality Plot | Compute |
| Summary Statistics | Compute |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 46.4 | 28.21 | 18.19 |
| 2 | 45.7 | 32.37 | 13.33 |
| 3 | 45.3 | 38.41 | 6.885 |
| 4 | 38.6 | 36.47 | 2.127 |
| 5 | 37.2 | 28.88 | 8.321 |
| 6 | 35 | 26.42 | 8.58 |
| 7 | 34 | 39.04 | -5.04 |
| 8 | 28.3 | 20.7 | 7.597 |
| 9 | 24.7 | 19.3 | 5.4 |
| 10 | 24.7 | 26.81 | -2.108 |
| 11 | 24.4 | 18.8 | 5.596 |
| 12 | 22.7 | 18.37 | 4.327 |
| 13 | 22.3 | 27.61 | -5.306 |
| 14 | 21.7 | 18.09 | 3.608 |
| 15 | 21.6 | 20.42 | 1.178 |
| 16 | 21.3 | 36.88 | -15.58 |
| 17 | 21.2 | 21.76 | -0.5598 |
| 18 | 20.8 | 23.51 | -2.707 |
| 19 | 20.3 | 25.62 | -5.322 |
| 20 | 18.9 | 23.01 | -4.111 |
| 21 | 18.8 | 23.66 | -4.858 |
| 22 | 18.6 | 18.11 | 0.4861 |
| 23 | 18 | 25.45 | -7.449 |
| 24 | 17.6 | 19.28 | -1.679 |
| 25 | 17 | 19.58 | -2.581 |
| 26 | 16.7 | 22.41 | -5.707 |
| 27 | 15.9 | 23.05 | -7.154 |
| 28 | 15.3 | 19.06 | -3.763 |
| 29 | 15 | 17.47 | -2.467 |
| 30 | 14.8 | 24.03 | -9.225 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 5 | 0.6282 | 0.7436 | 0.3718 |
| 6 | 0.7906 | 0.4188 | 0.2094 |
| 7 | 0.9443 | 0.1115 | 0.05573 |
| 8 | 0.9913 | 0.01737 | 0.008685 |
| 9 | 0.9963 | 0.007445 | 0.003722 |
| 10 | 0.9991 | 0.001767 | 0.0008833 |
| 11 | 0.9995 | 0.0009293 | 0.0004647 |
| 12 | 0.9997 | 0.0006398 | 0.0003199 |
| 13 | 0.9999 | 0.0002498 | 0.0001249 |
| 14 | 0.9999 | 0.0001917 | 9.586e-05 |
| 15 | 0.9999 | 0.000114 | 5.699e-05 |
| 16 | 1 | 3.492e-05 | 1.746e-05 |
| 17 | 1 | 2.785e-05 | 1.393e-05 |
| 18 | 1 | 2.879e-05 | 1.439e-05 |
| 19 | 1 | 3.754e-05 | 1.877e-05 |
| 20 | 1 | 8.458e-05 | 4.229e-05 |
| 21 | 0.9999 | 0.0001645 | 8.223e-05 |
| 22 | 0.9999 | 0.0002471 | 0.0001235 |
| 23 | 0.9997 | 0.0005692 | 0.0002846 |
| 24 | 0.9993 | 0.001434 | 0.0007172 |
| 25 | 0.9979 | 0.004291 | 0.002146 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 17 | 0.8095 | NOK |
| 5% type I error level | 18 | 0.857143 | NOK |
| 10% type I error level | 18 | 0.857143 | NOK |
| Ramsey RESET F-Test for powers (2 and 3) of fitted values |
> reset_test_fitted RESET test data: mylm RESET = 2.5152, df1 = 2, df2 = 26, p-value = 0.1003 |
| Ramsey RESET F-Test for powers (2 and 3) of regressors |
> reset_test_regressors RESET test data: mylm RESET = 2.5152, df1 = 2, df2 = 26, p-value = 0.1003 |
| Ramsey RESET F-Test for powers (2 and 3) of principal components |
> reset_test_principal_components RESET test data: mylm RESET = 2.5152, df1 = 2, df2 = 26, p-value = 0.1003 |
