Introduction:
In this analysis, I aims to explore the factors influencing sanitation coverage, utilizing both ANOVA and linear regression models. The dataset used for this analysis is derived from a CSV file containing information related to sanitation services in various regions. The tasks performed include summarizing the data, conducting ANOVA tests to assess the impact of categorical variables (such as service type and region) on sanitation coverage, and building a linear regression model to examine the relationship between a continuous variable (population) and sanitation coverage.

Summary of Data:
The data consists of various columns such as Type, Region, Residence Type, Service Type, Year, Coverage, Population, and Service Level.
The summary provides information about the distribution and range of each variable, including minimum, maximum, median, and quartiles.

ANOVA Test for Service Type:
An ANOVA test was conducted to determine if there is a significant difference in Coverage based on Service Type.
The test resulted in a highly significant p-value (<2e-16), indicating that Service Type has a significant impact on Coverage.

Consolidation of Regions:
To simplify analysis, regions were consolidated into broader categories if there were more than 10 distinct regions.
The ANOVA test conducted after consolidation did not yield significant results (p-value = 0.152), suggesting that the effect of region on Coverage may not be statistically significant.

Linear Regression Model:
A linear regression model was built with Coverage as the response variable and Population as the predictor variable.
The coefficients of the model indicate that both the intercept and Population are statistically significant predictors of Coverage.
The R-squared value of 0.3787 suggests that approximately 37.87% of the variability in Coverage can be explained by Population.
The scatter plot with the regression line visually represents the relationship between Population and Coverage. The increasing trend indicates that higher Population tends to be associated with higher Coverage.

Further Questions:
While the linear regression model suggests a significant relationship between Population and Coverage, it's essential to investigate other potential factors that might influence Coverage.
Exploring interactions between different variables and conducting more advanced modeling techniques could provide a more comprehensive understanding of the factors affecting Coverage.

Conclusion:
As I conducted the analysis, it's clear that sanitation coverage is influenced by various factors, including the region and type of service provided. From the ANOVA tests, it's clear that service type has a notable impact on sanitation coverage. This suggests that the type of sanitation service provided influences the overall coverage rate. However, the influence of region on coverage seems less pronounced, with statistical tests showing no significant difference in coverage rates among regions.
Furthermore, the linear regression model highlighted a strong positive relationship between population size and sanitation coverage. This finding suggests that areas with larger populations tend to have higher sanitation coverage, indicating the importance of scaling up sanitation infrastructure to accommodate growing populations effectively.

# Read the CSV file
data <- read.csv("C:\\Users\\am790\\Downloads\\washdash-download (1).csv")

# Summary of the data
summary(data)

##      Type              Region          Residence.Type     Service.Type      
##  Length:3367        Length:3367        Length:3367        Length:3367       
##  Class :character   Class :character   Class :character   Class :character  
##  Mode  :character   Mode  :character   Mode  :character   Mode  :character  
##                                                                             
##                                                                             
##                                                                             
##       Year         Coverage         Population        Service.level     
##  Min.   :2010   Min.   :  0.000   Min.   :0.000e+00   Length:3367       
##  1st Qu.:2013   1st Qu.:  2.486   1st Qu.:4.366e+06   Class :character  
##  Median :2016   Median : 12.110   Median :3.306e+07   Mode  :character  
##  Mean   :2016   Mean   : 22.447   Mean   :1.497e+08                     
##  3rd Qu.:2019   3rd Qu.: 34.190   3rd Qu.:1.755e+08                     
##  Max.   :2022   Max.   :100.000   Max.   :2.173e+09

options(scipen = 999)
# Convert 'Service Type' to a factor
data$Service.Type <- factor(data$Service.Type)

# Perform ANOVA test
anova_result <- aov(Coverage ~ Service.Type, data = data)

# Summary of ANOVA
summary(anova_result)

##                Df  Sum Sq Mean Sq F value              Pr(>F)    
## Service.Type    2   59612   29806   45.77 <0.0000000000000002 ***
## Residuals    3364 2190520     651                                
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

# Consolidate regions if there are more than 10 categories
library(dplyr)

## Warning: package 'dplyr' was built under R version 4.3.3

## 
## 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

data <- data %>%
  mutate(Region = ifelse(Region %in% c("Australia and New Zealand", "Europe", "Northern America"), "High-Income Regions", Region))

# Perform ANOVA test
anova_result <- aov(Coverage ~ Region, data = data)

# Summary of ANOVA
summary(anova_result)

##               Df  Sum Sq Mean Sq F value Pr(>F)
## Region         7    7148  1021.1   1.529  0.152
## Residuals   3359 2242984   667.8

# Build linear regression model
lm_model <- lm(Coverage ~ Population, data = data)

# Summary of the model
summary(lm_model)

## 
## Call:
## lm(formula = Coverage ~ Population, data = data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -48.550 -13.156  -8.551   6.778  86.106 
## 
## Coefficients:
##                    Estimate      Std. Error t value            Pr(>|t|)    
## (Intercept) 13.659504476453  0.401306997071   34.04 <0.0000000000000002 ***
## Population   0.000000058712  0.000000001296   45.29 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 20.38 on 3365 degrees of freedom
## Multiple R-squared:  0.3787, Adjusted R-squared:  0.3785 
## F-statistic:  2051 on 1 and 3365 DF,  p-value: < 0.00000000000000022

# Scatter plot
library(ggplot2)

## Warning: package 'ggplot2' was built under R version 4.3.3

ggplot(data, aes(x = Year, y = Coverage)) +
  geom_point() +
  geom_smooth(method = "lm", se = FALSE) +
  labs(x = "Year", y = "Coverage", title = "Relationship between Year and Coverage")

## `geom_smooth()` using formula = 'y ~ x'
plot of chunk unnamed-chunk-1
# Load necessary libraries
library(ggplot2)

# Scatter plot with regression line
ggplot(data, aes(x = Population, y = Coverage)) +
  geom_point() +  # Add points
  geom_smooth(method = "lm", se = FALSE) +  # Add regression line
  labs(x = "Population", y = "Coverage", title = "Linear Regression Model Visualization")

## `geom_smooth()` using formula = 'y ~ x'
plot of chunk unnamed-chunk-1