Midterm Q2

Hypotheses

• Hypothesis- Different ad versions have a significant impact on the number of purchases.

Loading Data

# Load necessary libraries
library(ggplot2)
library(dplyr)

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

# Creating the dataset
ab_testing <- data.frame(
  Ads = c(1,0,2,0,1,1,2,2,2,0,2,2,0,2,2,0,2,0,0,2,0,1,1,2,1,0,1,0,2),
  Purchase = c(152,21,77,65,183,87,121,104,116,82,53,91,85,53,51,25,81,23,42,54,84,124,106,14,61,24,118,39,70)
)

# View first few rows
head(ab_testing)

##   Ads Purchase
## 1   1      152
## 2   0       21
## 3   2       77
## 4   0       65
## 5   1      183
## 6   1       87

Exploratory Data Analysis

# Summary statistics
summary(ab_testing)

##       Ads           Purchase     
##  Min.   :0.000   Min.   : 14.00  
##  1st Qu.:0.000   1st Qu.: 51.00  
##  Median :1.000   Median : 77.00  
##  Mean   :1.069   Mean   : 76.07  
##  3rd Qu.:2.000   3rd Qu.:104.00  
##  Max.   :2.000   Max.   :183.00

# Boxplot 
ggplot(ab_testing, aes(x = factor(Ads), y = Purchase, fill = factor(Ads))) +
  geom_boxplot() +
  labs(title = "Distribution of Purchases by Ad Type", x = "Ad Type", y = "Number of Purchases") +
  theme_minimal()

Regression Analysis

# Running a linear regression model
model <- lm(Purchase ~ factor(Ads), data = ab_testing)
summary(model)

## 
## Call:
## lm(formula = Purchase ~ factor(Ads), data = ab_testing)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -59.75 -22.75  -3.75  30.25  64.29 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     49.00      10.21   4.800 5.69e-05 ***
## factor(Ads)1    69.71      15.91   4.383 0.000171 ***
## factor(Ads)2    24.75      13.82   1.791 0.084982 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 32.28 on 26 degrees of freedom
## Multiple R-squared:  0.4262, Adjusted R-squared:  0.3821 
## F-statistic: 9.656 on 2 and 26 DF,  p-value: 0.0007308

Interpretation & Managerial Recommendations

# Extracting model coefficients, p-value, and R-squared value
coefficients <- summary(model)$coefficients
p_values <- coefficients[,4]
r_squared <- summary(model)$r.squared

# Display results
coefficients

##              Estimate Std. Error  t value     Pr(>|t|)
## (Intercept)  49.00000   10.20740 4.800438 5.691154e-05
## factor(Ads)1 69.71429   15.90709 4.382592 1.714257e-04
## factor(Ads)2 24.75000   13.82089 1.790768 8.498177e-02

p_values

##  (Intercept) factor(Ads)1 factor(Ads)2 
## 5.691154e-05 1.714257e-04 8.498177e-02

r_squared

## [1] 0.4262103

• Coefficients Interpretation: On average Ad 1 increases purchases by 69.71 compared to the control group. The p-value (0.00017) is very low, indicating a statistically significant impact. On average, using Ad 2 increases purchases by 24.75 compared to the control group. However, the p-value (0.08498) is above 0.05, meaning this effect is not statistically significant.

• R-Squared Interpretation: Intercept p = 5.69e-05= Significant, confirming that the baseline purchases, are not zero.

• Managerial Recommendations:

  • Based on the data, Investing more into Ad 1 will result in higher profits as it performed better and was statistically more significant.