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
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.