The
Logistic Regression is a regression model in which the response
variable (dependent variable) has categorical values such as True/False
or 0/1. It actually measures the probability of a binary response as the
value of response variable based on the mathematical equation relating
it with the predictor variables.

The general mathematical equation for logistic regression is −

y = 1/(1+e^-(a+b1x1+b2x2+b3x3+...))

Following is the description of the parameters used −

**y**is the response variable.**x**is the predictor variable.**a**and**b**are the coefficients which are numeric constants.

The function used to create the regression model is the

**glm()**function.## Syntax

The basic syntax for

**glm()**function in logistic regression is −```
glm(formula,data,family)
```

Following is the description of the parameters used −

**formula**is the symbol presenting the relationship between the variables.**data**is the data set giving the values of these variables.**family**is R object to specify the details of the model. It's value is binomial for logistic regression.

## Example

The
in-built data set "mtcars" describes different models of a car with
their various engine specifications. In "mtcars" data set, the
transmission mode (automatic or manual) is described by the column am
which is a binary value (0 or 1). We can create a logistic regression
model between the columns "am" and 3 other columns - hp, wt and cyl.

# Select some columns form mtcars. input <- mtcars[,c("am","cyl","hp","wt")] print(head(input))

When we execute the above code, it produces the following result −

```
am cyl hp wt
Mazda RX4 1 6 110 2.620
Mazda RX4 Wag 1 6 110 2.875
Datsun 710 1 4 93 2.320
Hornet 4 Drive 0 6 110 3.215
Hornet Sportabout 0 8 175 3.440
Valiant 0 6 105 3.460
```

## Create Regression Model

We use the

**glm()**function to create the regression model and get its summary for analysis.input <- mtcars[,c("am","cyl","hp","wt")] am.data = glm(formula = am ~ cyl + hp + wt, data = input, family = binomial) print(summary(am.data))

When we execute the above code, it produces the following result −

```
Call:
glm(formula = am ~ cyl + hp + wt, family = binomial, data = input)
Deviance Residuals:
Min 1Q Median 3Q Max
-2.17272 -0.14907 -0.01464 0.14116 1.27641
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 19.70288 8.11637 2.428 0.0152 *
cyl 0.48760 1.07162 0.455 0.6491
hp 0.03259 0.01886 1.728 0.0840 .
wt -9.14947 4.15332 -2.203 0.0276 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 43.2297 on 31 degrees of freedom
Residual deviance: 9.8415 on 28 degrees of freedom
AIC: 17.841
Number of Fisher Scoring iterations: 8
```

### CONCLUSION

In
the summary as the p-value in the last column is more than 0.05 for the
variables "cyl" and "hp", we consider them to be insignificant in
contributing to the value of the variable "am". Only weight (wt) impacts
the "am" value in this regression model.

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