203.2.2 Logistic Function to Regression

Logistic Regression Function

In previous section, we studied about Logistic Regression, why do we need it?

Logistic regression models the logit of the outcome, instead of the outcome i.e. instead of winning or losing, we build a model for log odds of winning or losing
Natural logarithm of the odds of the outcome
ln(Probability of the outcome (p)/Probability of not having the outcome (1-p))

\[P(y|x) = \frac{e^{(\beta_0+ \beta_1X)}}{1+e^{($\beta_0+ \beta_1X)}}\]

Lab: Logistic Regression

1. Import Dataset: Product Sales Data/Product_sales.csv
1. Build a logistic Regression line between Age and buying
1. A 25 years old customer, will he buy the product?
1. If Age is 105 then will that customer buy the product?
1. Draw a scatter plot between Age and Buy. Include both linear and logistic regression lines on the same chart.

Logistic Regression in R

1. Import Dataset: Product Sales Data/Product_sales.csv

Product_sales<- read.csv("C:\\Amrita\\Datavedi\\Product Sales Data\\Product_sales.csv")

1. Build a logistic Regression line between Age and buying

prod_sales_Logit_model <- glm(Bought ~ Age,family=binomial(logit),data=Product_sales)
summary(prod_sales_Logit_model)

## 
## Call:
## glm(formula = Bought ~ Age, family = binomial(logit), data = Product_sales)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -3.6922  -0.1645  -0.0619   0.1246   3.5378  
## 
## Coefficients:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept) -6.90975    0.72755  -9.497   <2e-16 ***
## Age          0.21786    0.02091  10.418   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 640.425  on 466  degrees of freedom
## Residual deviance:  95.015  on 465  degrees of freedom
## AIC: 99.015
## 
## Number of Fisher Scoring iterations: 7

1. A 25 years old customer, will he buy the product?

new_data<-data.frame(Age=25)
predict(prod_sales_Logit_model,new_data,type="response")

##         1 
## 0.1879529

1. If Age is 105 then will that customer buy the product?

new_data<-data.frame(Age=105)
predict(prod_sales_Logit_model,new_data,type="response")

##         1 
## 0.9999999

1. Draw a scatter plot between Age and Buy. Include both linear and logistic regression lines on the same chart.

plot(Product_sales$Age,Product_sales$Bought,col = "blue")
curve(predict(prod_sales_Logit_model,data.frame(Age=x),type="resp"),add=TRUE)
abline(prod_sales_model, lwd = 5, col="red")

The next post is about multiple logistic regression.

27th January 2017