UNISTAT - the ultimate Excel statistics add-in

Logistic Regression in Excel with UNISTAT

The UNISTAT statistics add-in extends Excel with Logistic Regression capabilities.

For further information visit UNISTAT User's Guide section 7.2.6. Logistic Regression.

Here we provide a sample output from the UNISTAT Excel statistics add-in for data analysis.

Logistic Regression

Dependent Variable: GRADE
Minimum of dependent variable is encoded as 0 and the rest as 1.
Valid Number of Cases: 32, 0 Omitted

Regression Coefficients

CoefficientStandard ErrorWald StatisticProbabilityLower 95%Upper 95%
Constant-13.0213 4.9313 6.9724 0.0083-22.6866-3.3561
GPA 2.8261 1.2629 5.0074 0.0252 0.3508 5.3014
TUCE 0.0952 0.1416 0.4519 0.5014-0.1823 0.3726
PSI 2.3787 1.0646 4.9926 0.0255 0.2922 4.4652

Goodness of Fit Tests

-2 Log likelihood
Initial Model 41.1835
Final Model 25.7793

Chi-Square StatisticDegrees of FreedomRight-Tail Probability
Pearson 27.2571 27 0.4500
Likelihood Ratio 15.4042 3 0.0015
Hosmer-Lemeshow 7.4526 8 0.4887

Pseudo R-squared
McFadden 0.3740
Adjusted McFadden 0.1798
Cox & Snell 0.3821
Nagelkerke 0.5278

Correlation Matrix of Regression Coefficients

ConstantGPATUCEPSI
Constant 1.0000-0.7343-0.4960-0.4494
GPA-0.7343 1.0000-0.2065 0.3181
TUCE-0.4960-0.2065 1.0000 0.0990
PSI-0.4494 0.3181 0.0990 1.0000

Covariance Matrix of Regression Coefficients

ConstantGPATUCEPSI
Constant 24.3180-4.5735-0.3463-2.3592
GPA-4.5735 1.5950-0.0369 0.4276
TUCE-0.3463-0.0369 0.0200 0.0149
PSI-2.3592 0.4276 0.0149 1.1333

Odds Ratio

Odds RatioStandard ErrorLower 95%Upper 95%
GPA 16.8797 21.3181 1.4202 200.6239
TUCE 1.0998 0.1557 0.8334 1.4515
PSI 10.7907 11.4874 1.3393 86.9380

Hosmer-Lemeshow Table

Actual Y = 0Expected Y = 0Actual Y = 1Expected Y = 1Total
1 4 3.8965 0 0.1035 4
2 3 2.8964 0 0.1036 3
3 3 2.8353 0 0.1647 3
4 2 2.7165 1 0.2835 3
5 2 2.4295 1 0.5705 3
6 4 2.7678 0 1.2322 4
7 1 1.4199 2 1.5801 3
8 1 1.1139 2 1.8861 3
9 0 0.6265 3 2.3735 3
10 1 0.2977 2 2.7023 3

Case (Diagnostic) Statistics

Minimum of dependent variable is encoded as 0 and the rest as 1.

Actual YFitted YPredicted GroupLeverageCook’s DistanceDevianceResidualsStandardised Residuals
1 0.0000 0.0266 0.0000 0.0390 0.0011-0.2321-0.0266-0.1652
2 0.0000 0.0595 0.0000 0.0545 0.0036-0.3503-0.0595-0.2515
3 0.0000 0.1873 0.0000 0.0889 0.0225-0.6440-0.1873-0.4800
4 0.0000 0.0259 0.0000 0.0807 0.0023-0.2291-0.0259-0.1631
5 1.0000 0.5699 1.0000 0.3289 0.3698 1.0605 0.4301 0.8687
6 0.0000 0.0349 0.0000 0.0549 0.0021-0.2664-0.0349-0.1900
7 0.0000 0.0265 0.0000 0.0458 0.0013-0.2318-0.0265-0.1650
8 0.0000 0.0516 0.0000 0.0512 0.0029-0.3254-0.0516-0.2332
9 0.0000 0.1111 0.0000 0.0853 0.0117-0.4854-0.1111-0.3536
10 1.0000 0.6935 1.0000 0.2861 0.1771 0.8556 0.3065 0.6648
11 0.0000 0.0245 0.0000 0.0376 0.0010-0.2226-0.0245-0.1584
12 0.0000 0.1900 0.0000 0.0869 0.0223-0.6492-0.1900-0.4843
13 0.0000 0.3222 0.0000 0.1312 0.0718-0.8820-0.3222-0.6895
F- 14 1.0000 0.1932 0.0000 0.1002 0.4650 1.8133 0.8068 2.0434
15 0.0000 0.3610 0.0000 0.1540 0.1028-0.9464-0.3610-0.7516
16 0.0000 0.0302 0.0000 0.0428 0.0014-0.2476-0.0302-0.1764
17 0.0000 0.0536 0.0000 0.0690 0.0042-0.3320-0.0536-0.2380
18 0.0000 0.0386 0.0000 0.0487 0.0021-0.2805-0.0386-0.2003
F+ 19 0.0000 0.5899 1.0000 0.1085 0.1751-1.3351-0.5899-1.1993
20 1.0000 0.6608 1.0000 0.1303 0.0769 0.9103 0.3392 0.7165
21 0.0000 0.0614 0.0000 0.1263 0.0095-0.3559-0.0614-0.2557
22 1.0000 0.9048 1.0000 0.1109 0.0131 0.4472 0.0952 0.3243
23 0.0000 0.2418 0.0000 0.3215 0.1511-0.7440-0.2418-0.5647
F+ 24 0.0000 0.8521 1.0000 0.1080 0.6972-1.9551-0.8521-2.4002
25 1.0000 0.8383 1.0000 0.0992 0.0213 0.5940 0.1617 0.4392
26 1.0000 0.4811 1.0000 0.2782 0.4157 1.2096 0.5189 1.0385
27 1.0000 0.6354 1.0000 0.2835 0.2270 0.9523 0.3646 0.7575
28 0.0000 0.3072 0.0000 0.1852 0.1008-0.8568-0.3072-0.6659
29 1.0000 0.8417 1.0000 0.1303 0.0282 0.5871 0.1583 0.4337
30 1.0000 0.9453 1.0000 0.0853 0.0054 0.3353 0.0547 0.2405
F+ 31 0.0000 0.5291 1.0000 0.1171 0.1490-1.2273-0.5291-1.0600
F- 32 1.0000 0.1110 0.0000 0.1299 1.1953 2.0966 0.8890 2.8296
Logit ResidualsStudentised ResidualsDelta-Beta ConstantDelta-Beta GPADelta-Beta TUCEDelta-Beta PSI
1-1.0273-0.2368-0.1446 0.0296 0.0012 0.0255
2-1.0633-0.3602-0.2192 0.0488 0.0008 0.0500
3-1.2304-0.6747-0.2069 0.0468-0.0028 0.1231
4-1.0266-0.2389-0.1918 0.0101 0.0060 0.0262
5 1.7547 1.2945-0.7994 0.6609-0.0469-0.2150
6-1.0361-0.2740-0.1974 0.0236 0.0041 0.0326
7-1.0272-0.2373-0.1614 0.0222 0.0030 0.0257
8-1.0544-0.3340-0.2131 0.0419 0.0017 0.0445
9-1.1250-0.5075-0.2192 0.0806-0.0052 0.0839
10 1.4419 1.0126-1.5677 0.2612 0.0387-0.1075
11-1.0251-0.2269-0.1364 0.0284 0.0011 0.0238
12-1.2346-0.6794-0.2435 0.0265 0.0017 0.1241
13-1.4754-0.9463-0.0099-0.1007 0.0064 0.1816
F- 14 5.1757 1.9116 0.6743-0.2661 0.0308-0.5311
15-1.5649-1.0289 0.3538-0.0414-0.0189 0.1971
16-1.0311-0.2531-0.1642 0.0285 0.0021 0.0285
17-1.0567-0.3441-0.1777 0.0640-0.0031 0.0467
18-1.0401-0.2876-0.1945 0.0309 0.0028 0.0351
F+ 19-2.4383-1.4141 0.1815 0.0123-0.0095-0.2986
20 1.5133 0.9761-0.4484-0.0112 0.0206 0.1943
21-1.0654-0.3808-0.3456 0.1175-0.0023 0.0012
22 1.1052 0.4743-0.4594 0.0636 0.0103 0.0792
23-1.3189-0.9032-1.3875 0.0189 0.0561-0.0779
F+ 24-6.7609-2.0700 2.9581-0.4707-0.0574-0.6331
25 1.1929 0.6258-0.4563 0.1103 0.0034 0.1159
26 2.0784 1.4238-0.2394-0.4520 0.0756 0.2781
27 1.5738 1.1251 0.2892 0.3224-0.0590 0.2429
28-1.4435-0.9492-0.5420 0.2916-0.0192-0.1032
29 1.1881 0.6295-0.3651 0.1639-0.0082 0.1180
30 1.0578 0.3506-0.2569 0.0828-0.0011 0.0495
F+ 31-2.1237-1.3061-0.3054-0.0140 0.0150-0.2474
F- 32 9.0065 2.2477 4.5458-1.0577-0.0397 0.0812

F+: False Positive
F-: False Negative

2 x 2 Table

Estimated \ ActualPositiveNegativeTotal
Positive 9 3 12
81.82% 14.29%
Negative 2 18 20
18.18% 85.71%
Total 11 21 32
100.00% 100.00%

Classification Threshold Probability 0.4211

Statistics for Diagnostic Tests

Confidence Intervals: Row 1: Asymptotic Normal, Row 2: Exact Binomial

ValueStandard ErrorLower 95%Upper 95%
Sensitivity 0.8182 0.1163 0.5903 1.0000
0.4822 0.9772
Specificity 0.8571 0.0764 0.7075 1.0000
0.6366 0.9695
Accuracy 0.8438 0.0642 0.7179 0.9696
0.6721 0.9472
Prevalence 0.3438 0.0840 0.1792 0.5083
0.1857 0.5319
Apparent Prevalence 0.3750 0.0856 0.2073 0.5427
0.2110 0.5631
Youden’s Index 0.6753
0.1188 0.9467
Positive Predictive Value 0.7500 0.1250 0.5050 0.9950
0.4281 0.9451
Negative Predictive Value 0.9000 0.0671 0.7685 1.0000
0.6830 0.9877
Positive Likelihood Ratio 5.7273 1.9371 16.9334
Negative Likelihood Ratio 0.2121 0.0596 0.7547
Diagnostic Odds Ratio 27.0000 3.8033 191.6750
Weighted Positive Likelihood Ratio 3.0000 1.0678 8.4284
Weighted Negative Likelihood Ratio 0.1111 0.0295 0.4183

Logistic Regression

Dependent Variable: GRADE
Minimum of dependent variable is encoded as 0 and the rest as 1.
Valid Number of Cases: 32, 0 Omitted

Area Under the Curve

AUCStandard ErrorZ-Statistic1-Tail Probability2-Tail ProbabilityLower 95%Upper 95%
0.8831 0.0621 6.1721 0.0000 0.0000 0.7615 1.0048

ROC Table

* marks the best cut-off case.
Optimality criterion: Max(Sensitivity + Specificity)
Confidence Intervals: Asymptotic Normal

Cut-off P <=SensitivityLower 95%Upper 95%SpecificityLower 95%Upper 95%
1 0.9453 0.0909 0.0000 0.2608 1.0000 1.0000 1.0000
2 0.9048 0.1818 0.0000 0.4097 1.0000 1.0000 1.0000
3 0.8521 0.1818 0.0000 0.4097 0.9524 0.8613 1.0000
4 0.8417 0.2727 0.0095 0.5359 0.9524 0.8613 1.0000
5 0.8383 0.3636 0.0794 0.6479 0.9524 0.8613 1.0000
6 0.6935 0.4545 0.1603 0.7488 0.9524 0.8613 1.0000
7 0.6608 0.5455 0.2512 0.8397 0.9524 0.8613 1.0000
8 0.6354 0.6364 0.3521 0.9206 0.9524 0.8613 1.0000
9 0.5899 0.6364 0.3521 0.9206 0.9048 0.7792 1.0000
10 0.5699 0.7273 0.4641 0.9905 0.9048 0.7792 1.0000
11 0.5291 0.7273 0.4641 0.9905 0.8571 0.7075 1.0000
* 12 0.4811 0.8182 0.5903 1.0000 0.8571 0.7075 1.0000
13 0.3610 0.8182 0.5903 1.0000 0.8095 0.6416 0.9775
14 0.3222 0.8182 0.5903 1.0000 0.7619 0.5797 0.9441
15 0.3072 0.8182 0.5903 1.0000 0.7143 0.5211 0.9075
16 0.2418 0.8182 0.5903 1.0000 0.6667 0.4650 0.8683
17 0.1932 0.9091 0.7392 1.0000 0.6667 0.4650 0.8683
18 0.1900 0.9091 0.7392 1.0000 0.6190 0.4113 0.8267
19 0.1873 0.9091 0.7392 1.0000 0.5714 0.3598 0.7831
20 0.1111 0.9091 0.7392 1.0000 0.5238 0.3102 0.7374
21 0.1110 1.0000 1.0000 1.0000 0.5238 0.3102 0.7374
22 0.0614 1.0000 1.0000 1.0000 0.4762 0.2626 0.6898
23 0.0595 1.0000 1.0000 1.0000 0.4286 0.2169 0.6402
24 0.0536 1.0000 1.0000 1.0000 0.3810 0.1733 0.5887
25 0.0516 1.0000 1.0000 1.0000 0.3333 0.1317 0.5350
26 0.0386 1.0000 1.0000 1.0000 0.2857 0.0925 0.4789
27 0.0349 1.0000 1.0000 1.0000 0.2381 0.0559 0.4203
28 0.0302 1.0000 1.0000 1.0000 0.1905 0.0225 0.3584
29 0.0266 1.0000 1.0000 1.0000 0.1429 0.0000 0.2925
30 0.0265 1.0000 1.0000 1.0000 0.0952 0.0000 0.2208
31 0.0259 1.0000 1.0000 1.0000 0.0476 0.0000 0.1387
32 0.0245 1.0000 1.0000 1.0000 0.0000 0.0000 0.0000

Range of best Classification Threshold Probability 0.3610 <> 0.4811

Logistic Regression

Logistic Regression

Logistic Regression

Dependent Variable: GRADE
Minimum of dependent variable is encoded as 0 and the rest as 1.
Valid Number of Cases: 32, 0 Omitted

Area Under the Curve

AUCStandard ErrorZ-Statistic1-Tail Probability2-Tail ProbabilityLower 95%Upper 95%
GPA 0.7944 0.1001 2.9421 0.0016 0.0033 0.5983 0.9905
TUCE 0.6688 0.1075 1.5702 0.0582 0.1164 0.4581 0.8796
PSI 0.7208 0.0867 2.5477 0.0054 0.0108 0.5509 0.8906

Correlation Matrix of Areas

GPATUCEPSI
GPA 1.0000 0.2215-0.2182
TUCE 0.2215 1.0000-0.0997
PSI-0.2182-0.0997 1.0000

Covariance Matrix of Areas

GPATUCEPSI
GPA 0.0100 0.0024-0.0019
TUCE 0.0024 0.0116-0.0009
PSI-0.0019-0.0009 0.0075

Multiple Comparisons for Areas

DifferenceStandard ErrorZ-Statistic1-Tail Probability2-Tail ProbabilityLower 95%Upper 95%Chi-Square Statistic
GPA – TUCE 0.1255 0.1296 0.9684 0.1664 0.3328-0.1285 0.3796 0.9378
GPA – PSI 0.0736 0.1460 0.5042 0.3071 0.6141-0.2125 0.3597 0.2542
TUCE – PSI-0.0519 0.1447 0.3591 0.3598 0.7195-0.3355 0.2316 0.1289
Right-Tail Probability
GPA – TUCE 0.3328
GPA – PSI 0.6141
TUCE – PSI 0.7195

Logistic Regression