203.2.1 Logistic Regression, why do we need it?

LAB: Regression – Recap

• 1. Import Dataset: Product Sales Data/Product_sales.csv
• 2. What are the variables in the dataset?
• 3. Build a predictive model for Bought vs Age
• 4. What is R-Square?
• 5. If Age is 4 then will that customer buy the product?
• 6. If Age is 105 then will that customer buy the product?
• 7. Draw a scatter plot between Age and Buy. Include the regression line on the same chart.

Solution

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

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

• 2. What are the variables in the dataset?

names(Product_sales)

## [1] "Age"    "Bought"

• 3. Build a predictive model for Bought vs Age

prod_sales_model<-lm(Bought~Age,data=Product_sales)
summary(prod_sales_model)

## 
## Call:
## lm(formula = Bought ~ Age, data = Product_sales)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.14894 -0.12800 -0.01807  0.10759  1.10759 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.1704125  0.0152752  -11.16   <2e-16 ***
## Age          0.0209421  0.0004205   49.80   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1976 on 465 degrees of freedom
## Multiple R-squared:  0.8421, Adjusted R-squared:  0.8418 
## F-statistic:  2480 on 1 and 465 DF,  p-value: < 2.2e-16

• 4. What is R-Square?

0.8421 – 5. If Age is 4 then will that customer buy the product?

new_data<-data.frame(Age=4)
predict(prod_sales_model,new_data)

##           1 
## -0.08664394

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

new_data<-data.frame(Age=105)
predict(prod_sales_model,new_data)

##        1 
## 2.028511

• 7. Draw a scatter plot between Age and Buy. Include the regression line on the same chart.

plot(Product_sales$Age,Product_sales$Bought,col = "blue")
abline(prod_sales_model, lwd = 5, col="red")

What is the need of logistic regression?

• Consider Product sales data. The dataset has two columns.
• Age – continuous variable between 6-80
• Buy(0- Yes ; 1-No)

plot(Product_sales$Age,Product_sales$Bought,col = "blue")

Why not linear?

Some Nonlinear Functions

A Logistic Function

The Logistic Function

• We want a model that predicts probabilities between 0 and 1, that is, S-shaped.
• There are lots of s-shaped curves. We use the logistic model:
• \[Probability = \frac{e^{(\beta_0+ \beta_1X)}}{1+e^{($\beta_0+ \beta_1X)}}\]
• \[log_e(\frac{P}{1-P})=\beta_0+\beta_1X\]
• The function on left, \(log_e(\frac{P}{1-P})\), is called the logistic function.