# R Logistic Regression - r - learn r - r programming

• 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.
• r programming logistics regression

• The general mathematical equation for logistic regression is −
• 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 −
• 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.
• 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.
• 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.