CW2

R_CW2_Exploratory_and_Regression_Analysis

Introduction

GY7702 R for Data Science Course Work 2

library(dplyr) library(tidyverse) library(knitr) library(readr) library(lubridate) library(ggplot2) library(psych) library(Hmisc) library(corrplot) library(PerformanceAnalytics) library(car) library(magrittr) library(lmtest) library(usethis) library(gitcreds)

1.0 Loading and selecting data needed for analysis

#Loading in data for analysis OAC_Raw_uVariables_2011 <- read.csv("GY7702_2021-22_Assignment_2_v1-1_datapack/2011_OAC_Raw_uVariables-GY7702_2021-22_CW2.csv")

#Loading data that would be used to extract my Output Area LAD_Allocation_data <- read.csv("GY7702_2021-22_Assignment_2_v1-1_datapack/new.csv")

#Filtering out my allocated LAD LAD_Allocation_data <- LAD_Allocation_data %>% filter(LAD11CD == "E09000006")

#Joining the two data to select my allocated Output Area only OwnLadd <- LAD_Allocation_data %>% left_join( OAC_Raw_uVariables_2011, by = c("OA11CD" = "OA") ) %>% select(- c(LSOA11CD, LSO11ANM, MSOA11CD, MSOA11NM, LAD11CD, LAD11NM, LAD11NMW))

#Selecting variables needed for Analysis explorData <- OwnLadd %>% select( u104:u115, u159:u167)

1.1 Exploratory analysis of the data

describe(explorData,skew=TRUE, IQR = TRUE)

1.11 Showing the structure of the data

str(explorData) %>% knitr::kable()

1.12 Visualizing the distribution of the data with Histogram and QQ plot

par(mar=c(5,5,3,0)) ##This margin command should do the trick

explorData %>% gather() %>% ggplot2::ggplot( aes( x = value ) )+ ggplot2:: geom_histogram(binwidth = 5) + facet_wrap(~key, scales = 'free_x')

hist.data.frame(explorData)

for (i in 1:ncol(explorData)) { plt <- ggplot2::ggplot(explorData, aes( sample = explorData[,i] ) ) + ggplot2::stat_qq() + ggplot2::stat_qq_line()+ ggplot2::xlab(colnames( explorData[i])) print(plt)

}

1.13 Tranforming the data with Inverse hyperbolic sine function

for (i in 1:ncol(explorData)) { plt <- ggplot2::ggplot(explorData, aes( #adding inverse hyperbolic sine function sample = asinh(explorData[,i]) ) ) + ggplot2::stat_qq() + ggplot2::stat_qq_line()+ ggplot2::xlab(colnames( explorData[i])) print(plt)

}

1.21 Statistical approach to exploratory analysis and descriptive statistics of the data

stat_view <- explorData %>% pastecs::stat.desc(norm = TRUE) %>% round(5)

print(stat_view)

1.3 Kendall's regression correlation plot

corrplot(cor(explorData, method = "kendall"), type = "upper", tl.cex=0.5, method = 'shade', order = 'AOE', diag = FALSE, tl.col="black")

2.0 Part 2

2.11 Selecting the data needed for the regression analysis

regression_data <- OwnLadd %>% select( Total_Population, u104:u115, u159:u167) %>% #converting each column to represent percentage of population mutate( across(u104:u167, function(x){ (x/Total_Population)*100 }) ) %>% #renaming the variables rename_with( function(x){paste('perc', x, sep = "_")}, u104:u167 )

2.12 Checking the normality of the variables after normalizing them with percentage population

stat_view2 <- regression_data %>% pastecs::stat.desc(norm = TRUE) %>% round(5) print(stat_view2)

2.13 Selecting the variable to be used for the regression analysis

forregression <- regression_data %>% select(perc_u106, perc_u112, perc_u162)

2.21 Pearson correlation between variable perc_u106 and perc_u112

forregression %$% cor.test(perc_u106, perc_u112)

2.22 Pearson regression between variables perc_u106 and perc_u162

forregression %$% cor.test( perc_u106, perc_u162)

2.31 Regression analysis between variable perc_u106 (dependent) ~ perc_u114 + perc_u165(Independent)

health_model <- forregression %$% lm(perc_u106 ~ perc_u112 + perc_u162)

#2.32 Summary of the model summary(health_model)

- The p-value is 0.00001625: p-value < 0.01; Hence the model is significant.

We can reject the null hypothesis that none of the predictors have relationship with

the response variable.

# * This result is gotten by comparing the F-statistic to F distribution 11.15 where the

degrees of freedom is (2, 1017)

* F (2, 1017) = 11.15

* Adjusted R-squared = 0.01953

- Coefficient

* the coefficient = 30.79670 (significant)

# * The coefficient of slope for % of people with with Level 1, Level 2 or Apprenticeship

qualifications is estimated as 0.08282 (significant)

# * The coefficient of slope for % of people with with Administrative and secretarial

occupations is estimated as 0.16799 (Significant)

2.4 Test for normality, homoscedasticity, independence and multocollinearity

2.41 Test for normality

health_model %>% stats::rstandard() %>% stats::shapiro.test()

2.42 Test for homoscedasticity

health_model %>% lmtest::bptest()

2.43 Test for independence

health_model %>% lmtest::dwtest()

2.43 Test for multocollinearity

health_model %>% vif()

The output of the model indicates that the model fits **(F (2, 1017) = 11.15),

p-Value < 0.01**. However, the model on the percentage of people with Level 1, Level 2 or

Apprenticeship qualifications and people with Administrative and secretarial occupations

can only predict 2% of people with good health. The model have normally

distributed residuals (Shapiro-Wilk test, W=0.99, p=0.01678), no multicollinearity with

average VIF 1.028645, the residuals satisfy the assumption of homoscedasticity

(Breusch-Pagan test, BP = 1.7153, p-value = 0.4242) and assumptions of independence

(Durbin-Watson test, DW = 1.9789, p-value = 0.3613), However, we can say that the model

is partially robust because of the low adjusted R-squared value.

# Based on the result, the model indicates that for every one percent increase in the

percentage of people with with Level 1, Level 2 or Apprenticeship qualifications,

there will be 0.08282 increase in the percentage of people with good health.

Similarly, for every one percent increase in the percentage of people with

Administrative and secretarial occupations, there will be 0.16799 increase in the

percentage of people with good health.

2.51 Residual vs Fitted plot

health_model %>% plot(which = c(1))

2.51 gives an insight into the homoskedasticity of the residual. Since the red line is close

to the dash line, the linearity of the model seems to hold well, the model is homoskedastic as

the variance is not increasing, and point 770, 923 and 319 are outliers.

2.52 Normal Q-Q plot

health_model %>% plot(which = c(2))

2.52 shows the normality of the residuals. The fact that the qq plot lies on the line shows

that it is normally distributed.

2.53 Residual vs Leverage plot

health_model %>% plot(which = c(5))

2.53 gives insight about the Cook's distance. No point fall outside the Cook's Distance,

indicating that there is no influential point in the regression model.