Linear Regression in Excel with UNISTAT
The UNISTAT statistics add-in extends Excel with Linear Regression capabilities.
For further information visit UNISTAT User's Guide section 7.2.1. Linear Regression.
Here we provide a sample output from the UNISTAT Excel statistics add-in for data analysis.
Linear Regression
Dependent Variable: Systolic BP
Valid Number of Cases: 10, 0 Omitted
Regression Results
| Coefficient | Standard Error | t-Statistic | Probability | Lower 95% | Upper 95% | |
|---|---|---|---|---|---|---|
| Constant | 2.1276 | 2.0845 | 1.0207 | 0.3468 | -2.9729 | 7.2282 |
| Haemoglobin | 0.7859 | 1.3188 | 0.5959 | 0.5730 | -2.4412 | 4.0130 |
| Platelets | 2.6529 | 1.6012 | 1.6569 | 0.1486 | -1.2650 | 6.5709 |
| log Leucocytes | -2.4889 | 1.3651 | -1.8232 | 0.1181 | -5.8293 | 0.8514 |
| Residual Sum of Squares | 167.5104 |
|---|---|
| Standard Error | 5.2838 |
| Mean of Y | 3.1000 |
| Standard Deviation of Y | 6.1545 |
| Correlation Coefficient | 0.7132 |
| R-squared | 0.5086 |
| Adjusted R-squared | 0.2629 |
| F(3,6) | 2.0702 |
| Probability of F | 0.2057 |
| Durbin-Watson Statistic | 2.1713 |
| Log of Likelihood | -28.8358 |
| Press Statistic | 378.0616 |
ANOVA of Regression
| Due To | Sum of Squares | DoF | Mean Square | F-Stat | Prob |
|---|---|---|---|---|---|
| Haemoglobin | 54.267 | 1 | 54.267 | 1.944 | 0.2127 |
| Platelets | 26.318 | 1 | 26.318 | 0.943 | 0.3691 |
| log Leucocytes | 92.805 | 1 | 92.805 | 3.324 | 0.1181 |
| Regression | 173.390 | 3 | 57.797 | 2.070 | 0.2057 |
| Error | 167.510 | 6 | 27.918 | ||
| Total | 340.900 | 9 | 37.878 | 1.357 | 0.3667 |
Correlation Matrix of Regression Coefficients
| Constant | Haemoglobin | Platelets | log Leucocytes | |
|---|---|---|---|---|
| Constant | 1.0000 | 0.4886 | -0.1814 | 0.5119 |
| Haemoglobin | 0.4886 | 1.0000 | -0.1174 | 0.4037 |
| Platelets | -0.1814 | -0.1174 | 1.0000 | -0.4273 |
| log Leucocytes | 0.5119 | 0.4037 | -0.4273 | 1.0000 |
Covariance Matrix of Regression Coefficients
| Constant | Haemoglobin | Platelets | log Leucocytes | |
|---|---|---|---|---|
| Constant | 4.3450 | 1.3432 | -0.6055 | 1.4567 |
| Haemoglobin | 1.3432 | 1.7393 | -0.2479 | 0.7267 |
| Platelets | -0.6055 | -0.2479 | 2.5638 | -0.9340 |
| log Leucocytes | 1.4567 | 0.7267 | -0.9340 | 1.8636 |
Case (Diagnostic) Statistics
| Actual Y | Fitted Y | 95% lb Actual Y | 95% ub Actual Y | 95% lb Mean of Y | 95% ub Mean of Y | Standard Error of Fitted | Standardised Fitted | |
|---|---|---|---|---|---|---|---|---|
| 1 | -6.0000 | -2.7653 | -18.5949 | 13.0643 | -11.8987 | 6.3681 | 3.7326 | -1.3363 |
| 2 | 14.0000 | 11.1435 | -4.7617 | 27.0486 | 1.8798 | 20.4071 | 3.7858 | 1.8325 |
| 3 | 2.0000 | 2.7798 | -13.2188 | 18.7785 | -6.6434 | 12.2031 | 3.8511 | -0.0729 |
| 4 | 5.0000 | 2.1279 | -12.5920 | 16.8478 | -4.9089 | 9.1647 | 2.8758 | -0.2215 |
| 5 | 0.0000 | -2.7453 | -17.7949 | 12.3044 | -10.4481 | 4.9576 | 3.1480 | -1.3317 |
| 6 | 10.0000 | 3.4313 | -10.3709 | 17.2334 | -1.4001 | 8.2626 | 1.9745 | 0.0755 |
| 7 | -2.0000 | 1.2170 | -13.7152 | 16.1492 | -6.2539 | 8.6878 | 3.0532 | -0.4290 |
| 8 | 2.0000 | 1.5180 | -14.1130 | 17.1489 | -7.2666 | 10.3025 | 3.5901 | -0.3604 |
| 9 | -2.0000 | 6.8570 | -8.1138 | 21.8278 | -0.6906 | 14.4047 | 3.0846 | 0.8560 |
| 10 | 8.0000 | 7.4362 | -8.5519 | 23.4242 | -1.9691 | 16.8415 | 3.8437 | 0.9879 |
| Adjusted Fitted | Residuals | Standard Error of Residuals | Standardised Residuals | Studentised Residuals | Press (Deleted) Residuals | Studentised Press Residuals | Leverage | |
| 1 | 0.4570 | * | 3.7398 | -0.6122 | -0.8649 | -6.4570 | -0.8439 | 0.3990 |
| 2 | 8.1299 | * | 3.6859 | 0.5406 | 0.7750 | 5.8701 | 0.7458 | 0.4134 |
| 3 | 3.6636 | * | 3.6177 | -0.1476 | -0.2156 | -1.6636 | -0.1975 | 0.4312 |
| 4 | 0.9190 | * | 4.4326 | 0.5436 | 0.6479 | 4.0810 | 0.6133 | 0.1962 |
| 5 | -4.2559 | * | 4.2437 | 0.5196 | 0.6469 | 4.2559 | 0.6123 | 0.2550 |
| 6 | 2.3652 | * | 4.9010 | 1.2432 | 1.3403 | 7.6348 | 1.4617 | 0.0396 |
| 7 | 2.8295 | * | 4.3124 | -0.6088 | -0.7460 | -4.8295 | -0.7150 | 0.2339 |
| 8 | 1.1046 | * | 3.8768 | 0.0912 | 0.1243 | 0.8954 | 0.1136 | 0.3617 |
| 9 | 11.4359 | * | 4.2900 | -1.6763 | -2.0646 | -13.4359 | -3.5023 | 0.2408 |
| 10 | 6.8024 | * | 3.6255 | 0.1067 | 0.1555 | 1.1976 | 0.1423 | 0.4292 |
| Cook’s Distance | Mahalanobis Distance | Welsch Distance | Covratio | DfFit | Standardised DfFit | Delta-Beta Constant | Delta-Beta Haemoglobin | |
| 1 | 0.1863 | 3.5914 | -3.5703 | 2.4298 | -3.2223 | -0.8423 | -1.4482 | -0.5193 |
| 2 | 0.1584 | 3.7204 | 3.2943 | 2.7945 | 3.0136 | 0.7660 | 0.2032 | 0.1539 |
| 3 | 0.0132 | 3.8810 | -0.9214 | 4.2880 | -0.8837 | -0.2103 | -0.3219 | -0.1049 |
| 4 | 0.0442 | 1.7660 | 1.4230 | 2.2043 | 1.2089 | 0.3979 | 0.0843 | -0.4348 |
| 5 | 0.0576 | 2.2946 | 1.6966 | 2.4073 | 1.5107 | 0.4542 | 0.4374 | -0.2987 |
| 6 | 0.0729 | 0.3568 | 1.9046 | 0.5807 | 1.0661 | 0.5889 | 0.6419 | -0.1888 |
| 7 | 0.0697 | 2.1051 | -1.8606 | 2.1091 | -1.6126 | -0.5062 | -0.1466 | 0.3601 |
| 8 | 0.0033 | 3.2549 | 0.4303 | 3.8122 | 0.4134 | 0.1052 | 0.0840 | 0.0116 |
| 9 | 0.5509 | 2.1672 | -9.3048 | 0.0221 | -4.5789 | -2.5182 | -0.2646 | 0.8510 |
| 10 | 0.0068 | 3.8628 | 0.6594 | 4.3338 | 0.6338 | 0.1508 | 0.2351 | 0.1876 |
| Delta-Beta Platelets | Delta-Beta log Leucocytes | Standardised Delta-Beta Constant | Standardised Delta-Beta Haemoglobin | Standardised Delta-Beta Platelets | Standardised Delta-Beta log Leucocytes | |||
| 1 | 0.9274 | -0.9408 | -0.6779 | -0.3842 | 0.5651 | -0.6724 | ||
| 2 | 0.5029 | -0.8144 | 0.0938 | 0.1123 | 0.3022 | -0.5741 | ||
| 3 | -0.1625 | -0.1612 | -0.1415 | -0.0729 | -0.0930 | -0.1082 | ||
| 4 | 0.1857 | -0.1677 | 0.0383 | -0.3121 | 0.1098 | -0.1163 | ||
| 5 | -0.1725 | 0.2971 | 0.1986 | -0.2143 | -0.1019 | 0.2060 | ||
| 6 | 0.3740 | -0.0556 | 0.3358 | -0.1561 | 0.2547 | -0.0444 | ||
| 7 | 0.4028 | 0.2262 | -0.0674 | 0.2617 | 0.2411 | 0.1588 | ||
| 8 | -0.1374 | -0.0129 | 0.0368 | 0.0081 | -0.0784 | -0.0086 | ||
| 9 | -1.7818 | 1.1549 | -0.2154 | 1.0946 | -1.8878 | 1.4351 | ||
| 10 | 0.0126 | 0.0263 | 0.1032 | 0.1301 | 0.0072 | 0.0176 |
Linear Regression
Dependent Variable: AUC
Valid Number of Cases: 24, 0 Omitted
Regression Results
| Coefficient | Standard Error | t-Statistic | Probability | Lower 95% | Upper 95% | |
|---|---|---|---|---|---|---|
| Constant | 177.0000 | 20.3327 | 8.7052 | 0.0000 | 134.5868 | 219.4132 |
| Sequence = AB | -19.6667 | 28.7548 | -0.6839 | 0.5019 | -79.6480 | 40.3147 |
| Treatment = A | -5.1667 | 28.7548 | -0.1797 | 0.8592 | -65.1480 | 54.8147 |
| Sequence x Treatment = AB x A | 94.8333 | 40.6654 | 2.3320 | 0.0303 | 10.0069 | 179.6598 |
| Residual Sum of Squares | 49610.1667 |
|---|---|
| Standard Error | 49.8047 |
| Mean of Y | 188.2917 |
| Standard Deviation of Y | 58.3956 |
| Correlation Coefficient | 0.6062 |
| R-squared | 0.3675 |
| Adjusted R-squared | 0.2726 |
| F(3,20) | 3.8730 |
| Probability of F | 0.0247 |
| Durbin-Watson Statistic | 1.5155 |
| Log of Likelihood | -125.8492 |
| Press Statistic | 71438.6400 |
ANOVA of Regression
| Due To | Sum of Squares | DoF | Mean Square | F-Stat | Prob |
|---|---|---|---|---|---|
| Sequence = AB | 4620.375 | 1 | 4620.375 | 1.863 | 0.1875 |
| Treatment = A | 10710.375 | 1 | 10710.375 | 4.318 | 0.0508 |
| Sequence x Treatment = AB x A | 13490.042 | 1 | 13490.042 | 5.438 | 0.0303 |
| Regression | 28820.792 | 3 | 9606.931 | 3.873 | 0.0247 |
| Error | 49610.167 | 20 | 2480.508 | ||
| Total | 78430.958 | 23 | 3410.042 | 1.375 | 0.2378 |