8:46 a.m.
Hi,
Here x indicates income, N indicates number of families, n indicates number of families
with houses. How to run logistic regression if the data has frequencies?
X(000's$) Ni ni
6 40 8
8 50 12
10 60 18
13 80 28
15 100 45
20 70 36
25 65 39
30 50 33
35 40 30
40 25 20
11:16 a.m.
On 15/03/2026 09:46, Ramki S wrote:
Hi,
Here x indicates income, N indicates number of families, n indicates number of families
with houses. How to run logistic regression if the data has frequencies?
X(000's$) Ni ni
6 40 8
8 50 12
10 60 18
13 80 28
15 100 45
20 70 36
25 65 39
30 50 33
35 40 30
40 25 20
Hmmmm, maybe I'm missing the point, but what's wrong with the following?
<hansl>
series y = ni/Ni
logistic y const X000s
</hansl>
-------------------------------------------------------
Riccardo (Jack) Lucchetti
Dipartimento di Scienze Economiche e Sociali (DiSES)
Università Politecnica delle Marche
(formerly known as Università di Ancona)
r.lucchetti(a)univpm.it
http://www2.econ.univpm.it/servizi/hpp/lucchetti
-------------------------------------------------------
11:32 a.m.
Thanks for your reply. The following is the output by gujarati and porter. I am finding it
difficult to understand the weight (w) here and interpreting the coefficients. Any help?
ˆ ∗
Li = −1.59474√wi + 0.07862Xi∗
se = (0.11046) (0.00539)
t = (−14.43619) (14.56675) R2 = 0.9642
X Ni ni pi_hat 1 - pi_hat pi_hat / (1 - pi_hat) Li = ln(pi_hat / (1 - pi_hat)) wi =
Ni pi_hat (1 - pi_hat) sqrt(wi) = sqrt(Ni pi_hat (1 - pi_hat)) Li* = Li sqrt(wi) Xi* =
Xi sqrt(wi)
6 40 8 0.20 0.80 0.25 -1.3863 6.40 2.5298 -3.5077 15.1788
8 50 21 0.42 0.58 0.72 -1.1526 9.12 3.0199 -3.4801 24.1592
10 60 18 0.30 0.70 0.43 -0.8472 12.60 3.5496 -3.0072 35.4960
13 80 33 0.35 0.65 0.54 -0.6190 18.20 4.2661 -2.6404 55.4593
15 100 45 0.45 0.55 0.82 -0.2007 24.75 4.9749 -0.9985 74.6235
20 70 51 0.51 0.49 1.04 0.0500 17.49 4.1816 0.1673 83.6506
25 65 36 0.60 0.40 1.50 0.4055 15.60 3.9497 1.6012 98.7425
30 50 33 0.66 0.34 1.94 0.6633 11.20 3.3496 2.2218 100.4880
35 40 30 0.75 0.25 3.0 1.0986 7.50 2.7386 3.0070 95.8505
40 25 20 0.80 0.20 4.0 1.3863 4.00 2.0000 2.7726 80.0000
________
Gretl output as suggested by you:
gretl version 2026a
Current session: 2026-03-15 16:49
? series y = N/n_house
Generated series y (ID 4)
? logistic y const X_inc
Model 1: Logistic, using observations 1-10
Dependent variable: y
yhat =~ E(100 / (1 + exp(-X*b)))
coefficient std. error t-ratio p-value
--------------------------------------------------------
const −2.95413 0.107181 −27.56 3.24e-09 ***
X_inc −0.0399131 0.00463646 −8.609 2.57e-05 ***
Statistics based on the transformed data:
Sum squared resid 0.217306 S.E. of regression 0.164813
R-squared 0.902566 Adjusted R-squared 0.890387
F(1, 8) 74.10703 P-value(F) 0.000026
Log-likelihood 4.955783 Akaike criterion −5.911567
Schwarz criterion −5.306396 Hannan-Quinn −6.575437
Statistics based on the original data:
Mean dependent var 2.528896 S.D. dependent var 1.283018
Sum squared resid 9.461319 S.E. of regression 1.087504
1:09 p.m.
Below you have, for the dependent variable in gretl: "series y =
N/n_house" (which I guess means Ni/ni, with a switch of notation).
That's the wrong way round, it should be ni/Ni, giving values between
0 and 1.
There's reasonably explicit documentation of what gretl's "logistic"
command does, in the Command reference. Evidently, the software used
by Gujarati and Porter does something substantially different. I'm not
sure we can help in understanding what that is.
Allin Cottrell
On Sun, Mar 15, 2026 at 7:32 AM Ramki S <ramakrishnasalagrama(a)gmail.com> wrote:
>
> Thanks for your reply. The following is the output by gujarati and porter. I am
finding it difficult to understand the weight (w) here and interpreting the coefficients.
Any help?
>
> ˆ ∗
> Li = −1.59474√wi + 0.07862Xi∗
> se = (0.11046) (0.00539)
> t = (−14.43619) (14.56675) R2 = 0.9642
>
> X Ni ni pi_hat 1 - pi_hat
pi_hat / (1 - pi_hat) Li = ln(pi_hat / (1 - pi_hat)) wi = Ni pi_hat (1
- pi_hat) sqrt(wi) = sqrt(Ni pi_hat (1 - pi_hat)) Li* = Li sqrt(wi)
Xi* = Xi sqrt(wi)
>
> 6 40 8 0.20 0.80 0.25
-1.3863 6.40 2.5298 -3.5077 15.1788
> 8 50 21 0.42 0.58 0.72
-1.1526 9.12 3.0199 -3.4801 24.1592
> 10 60 18 0.30 0.70 0.43
-0.8472 12.60 3.5496 -3.0072 35.4960
> 13 80 33 0.35 0.65 0.54
-0.6190 18.20 4.2661 -2.6404 55.4593
> 15 100 45 0.45 0.55 0.82
-0.2007 24.75 4.9749 -0.9985 74.6235
> 20 70 51 0.51 0.49 1.04
0.0500 17.49 4.1816 0.1673 83.6506
> 25 65 36 0.60 0.40 1.50
0.4055 15.60 3.9497 1.6012 98.7425
> 30 50 33 0.66 0.34 1.94
0.6633 11.20 3.3496 2.2218 100.4880
> 35 40 30 0.75 0.25 3.0
1.0986 7.50 2.7386 3.0070 95.8505
> 40 25 20 0.80 0.20 4.0
1.3863 4.00 2.0000 2.7726 80.0000
>
> ________
> Gretl output as suggested by you:
> gretl version 2026a
> Current session: 2026-03-15 16:49
>
> ? series y = N/n_house
> Generated series y (ID 4)
> ? logistic y const X_inc
>
> Model 1: Logistic, using observations 1-10
> Dependent variable: y
> yhat =~ E(100 / (1 + exp(-X*b)))
>
> coefficient std. error t-ratio p-value
> --------------------------------------------------------
> const −2.95413 0.107181 −27.56 3.24e-09 ***
> X_inc −0.0399131 0.00463646 −8.609 2.57e-05 ***
>
> Statistics based on the transformed data:
>
> Sum squared resid 0.217306 S.E. of regression 0.164813
> R-squared 0.902566 Adjusted R-squared 0.890387
> F(1, 8) 74.10703 P-value(F) 0.000026
> Log-likelihood 4.955783 Akaike criterion −5.911567
> Schwarz criterion −5.306396 Hannan-Quinn −6.575437
>
> Statistics based on the original data:
>
> Mean dependent var 2.528896 S.D. dependent var 1.283018
> Sum squared resid 9.461319 S.E. of regression 1.087504
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3 comments
3 participants
participants (3)
-
Cottrell, Allin -
Ramki S -
Riccardo (Jack) Lucchetti