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StatBox 4.2

# Example Session using logist

`logist` performs logistic regression.

```» help logist

LOGIST Fit logistic regression model.
[BETA,MU,DEV,DF,SE]=LOGIST(Y,N,X,OFFSET,PRINT)
All input and output arguments except Y are optional.

Y - response vector containing binomial counts
N - number of trials for each count. Y is assumed to be binomial(p,N).
X - matrix of covariates, including the constant vector if required
OFFSET - offset if required
PRINT - enter any argument if output required each iteration

BETA - regression parameter estimates
SE - associated standard errors
MU - fitted values
DEV - residual deviance
DF - residual degrees of freedom```

A simple logistic regression. The counts are out of 10 in each case and there is one covariate.

```» y=[2 0 3 1 5 5 6 9 5 9];
» n=[10 10 10 10 10 10 10 10 10 10];
» x=(1:10)';
» X=[ones(10,1) x]
X =
1     1
1     2
1     3
1     4
1     5
1     6
1     7
1     8
1     9
1    10
» [beta mu dev df se]=logist(y,n,X)
beta =
-2.5800
0.4202

mu =
1.0342
1.4936
2.1092
2.8921
3.8249
4.8530
5.8937
6.8602
7.6884
8.3507

dev =
13.5505

df =
8

se =
0.5839
0.0923```

Here is the same regression using a different statistical program, namely R. The same results are obtained.

```> y <- c(2,0,3,1,5,5,6,9,5,9);
> n <- rep(10,10);
> x <- 1:10
> out <- glm(y/n ~ x,family=binomial,weights=n)
> summary(out)

Call:
glm(formula = y/n ~ x, family = binomial, weights = n)

Deviance Residuals:
Min       1Q   Median       3Q      Max
-1.8472  -1.0761   0.3411   0.7306   1.6120

Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -2.58000    0.58390  -4.419 9.94e-06 ***
x            0.42020    0.09228   4.554 5.27e-06 ***
---
Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1

(Dispersion parameter for binomial family taken to be 1)

Null deviance: 40.848  on 9  degrees of freedom
Residual deviance: 13.551  on 8  degrees of freedom
AIC: 39.455

Number of Fisher Scoring iterations: 4```

## References

Collett, D. (2002). Modelling Binary Data, 2nd edn. Chapman & Hall, London.