# 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.
- The general mathematical equation for logistic regression is −

r programming logistics regression

- 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.