HomeWork9
Marvellous Onajobi
2025-11-27
Description
- This project provides an analytical examination of global country data through the application of linear and multiple linear regression models. The objective is to determine which variables serve as the strongest predictors and contribute most effectively to the strength and reliability of the overall analysis.
# Load required libraries
library(tidyverse)## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.4 ✔ readr 2.1.5
## ✔ forcats 1.0.1 ✔ stringr 1.5.1
## ✔ ggplot2 4.0.0 ✔ tibble 3.3.0
## ✔ lubridate 1.9.4 ✔ tidyr 1.3.1
## ✔ purrr 1.1.0
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorslibrary(dplyr)
library(ggplot2)
library(broom)
library(car)## Loading required package: carData
##
## Attaching package: 'car'
##
## The following object is masked from 'package:dplyr':
##
## recode
##
## The following object is masked from 'package:purrr':
##
## some# Load dataset
setwd("~/Downloads/25_Semesters/Fall/DATA101")
df <- read_csv("AllCountries.csv")## Rows: 217 Columns: 26
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (2): Country, Code
## dbl (24): LandArea, Population, Density, GDP, Rural, CO2, PumpPrice, Militar...
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.# Inspect structure
str(df)## spc_tbl_ [217 × 26] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
## $ Country : chr [1:217] "Afghanistan" "Albania" "Algeria" "American Samoa" ...
## $ Code : chr [1:217] "AFG" "ALB" "DZA" "ASM" ...
## $ LandArea : num [1:217] 652.86 27.4 2381.74 0.2 0.47 ...
## $ Population : num [1:217] 37.172 2.866 42.228 0.055 0.077 ...
## $ Density : num [1:217] 56.9 104.6 17.7 277.3 163.8 ...
## $ GDP : num [1:217] 521 5254 4279 NA 42030 ...
## $ Rural : num [1:217] 74.5 39.7 27.4 12.8 11.9 34.5 75.4 8.1 36.9 56.6 ...
## $ CO2 : num [1:217] 0.29 1.98 3.74 NA 5.83 1.29 5.74 4.78 1.9 8.41 ...
## $ PumpPrice : num [1:217] 0.7 1.36 0.28 NA NA 0.97 NA 1.1 0.77 NA ...
## $ Military : num [1:217] 3.72 4.08 13.81 NA NA ...
## $ Health : num [1:217] 2.01 9.51 10.73 NA 14.02 ...
## $ ArmedForces : num [1:217] 323 9 317 NA NA 117 0 105 49 NA ...
## $ Internet : num [1:217] 11.4 71.8 47.7 NA 98.9 14.3 76 75.8 69.7 97.2 ...
## $ Cell : num [1:217] 67.4 123.7 111 NA 104.4 ...
## $ HIV : num [1:217] NA 0.1 0.1 NA NA 1.9 NA 0.4 0.2 NA ...
## $ Hunger : num [1:217] 30.3 5.5 4.7 NA NA 23.9 NA 3.8 4.3 NA ...
## $ Diabetes : num [1:217] 9.6 10.1 6.7 NA 8 3.9 13.2 5.5 7.1 11.6 ...
## $ BirthRate : num [1:217] 32.5 11.7 22.3 NA NA 41.3 16.1 17 13.1 11 ...
## $ DeathRate : num [1:217] 6.6 7.5 4.8 NA NA 8.4 5.8 7.6 9.7 8.9 ...
## $ ElderlyPop : num [1:217] 2.6 13.6 6.4 NA NA 2.5 7.2 11.3 11.4 13.6 ...
## $ LifeExpectancy: num [1:217] 64 78.5 76.3 NA NA 61.8 76.5 76.7 74.8 76 ...
## $ FemaleLabor : num [1:217] 50.3 55.9 16.4 NA NA 76.4 NA 57.1 55.8 NA ...
## $ Unemployment : num [1:217] 1.5 13.9 12.1 NA NA 7.3 NA 9.5 17.7 NA ...
## $ Energy : num [1:217] NA 808 1328 NA NA ...
## $ Electricity : num [1:217] NA 2309 1363 NA NA ...
## $ Developed : num [1:217] NA 1 1 NA NA 1 NA 2 1 NA ...
## - attr(*, "spec")=
## .. cols(
## .. Country = col_character(),
## .. Code = col_character(),
## .. LandArea = col_double(),
## .. Population = col_double(),
## .. Density = col_double(),
## .. GDP = col_double(),
## .. Rural = col_double(),
## .. CO2 = col_double(),
## .. PumpPrice = col_double(),
## .. Military = col_double(),
## .. Health = col_double(),
## .. ArmedForces = col_double(),
## .. Internet = col_double(),
## .. Cell = col_double(),
## .. HIV = col_double(),
## .. Hunger = col_double(),
## .. Diabetes = col_double(),
## .. BirthRate = col_double(),
## .. DeathRate = col_double(),
## .. ElderlyPop = col_double(),
## .. LifeExpectancy = col_double(),
## .. FemaleLabor = col_double(),
## .. Unemployment = col_double(),
## .. Energy = col_double(),
## .. Electricity = col_double(),
## .. Developed = col_double()
## .. )
## - attr(*, "problems")=<externalptr># Summary statistics
summary(df)## Country Code LandArea Population
## Length:217 Length:217 Min. : 0.01 Min. : 0.0120
## Class :character Class :character 1st Qu.: 10.83 1st Qu.: 0.7728
## Mode :character Mode :character Median : 94.28 Median : 6.5725
## Mean : 608.38 Mean : 35.0335
## 3rd Qu.: 446.30 3rd Qu.: 25.0113
## Max. :16376.87 Max. :1392.7300
## NA's :8 NA's :1
## Density GDP Rural CO2
## Min. : 0.1 Min. : 275 Min. : 0.00 Min. : 0.0400
## 1st Qu.: 37.5 1st Qu.: 2032 1st Qu.:19.62 1st Qu.: 0.8575
## Median : 92.1 Median : 5950 Median :38.15 Median : 2.7550
## Mean : 361.4 Mean : 14733 Mean :39.10 Mean : 4.9780
## 3rd Qu.: 219.8 3rd Qu.: 17298 3rd Qu.:57.83 3rd Qu.: 6.2525
## Max. :20777.5 Max. :114340 Max. :87.00 Max. :43.8600
## NA's :8 NA's :30 NA's :3 NA's :13
## PumpPrice Military Health ArmedForces
## Min. :0.1100 Min. : 0.000 Min. : 0.000 Min. : 0.0
## 1st Qu.:0.7450 1st Qu.: 3.015 1st Qu.: 6.157 1st Qu.: 12.0
## Median :0.9800 Median : 4.650 Median : 9.605 Median : 31.5
## Mean :0.9851 Mean : 6.178 Mean :10.597 Mean : 162.1
## 3rd Qu.:1.1800 3rd Qu.: 8.445 3rd Qu.:13.713 3rd Qu.: 146.5
## Max. :2.0000 Max. :31.900 Max. :39.460 Max. :3031.0
## NA's :50 NA's :67 NA's :29 NA's :49
## Internet Cell HIV Hunger
## Min. : 1.30 Min. : 13.70 Min. : 0.100 Min. : 2.50
## 1st Qu.:29.18 1st Qu.: 83.83 1st Qu.: 0.175 1st Qu.: 2.50
## Median :58.35 Median :110.00 Median : 0.400 Median : 6.50
## Mean :54.47 Mean :107.05 Mean : 1.941 Mean :11.25
## 3rd Qu.:78.92 3rd Qu.:127.50 3rd Qu.: 1.400 3rd Qu.:14.80
## Max. :98.90 Max. :328.80 Max. :27.400 Max. :61.80
## NA's :13 NA's :15 NA's :81 NA's :52
## Diabetes BirthRate DeathRate ElderlyPop
## Min. : 1.000 Min. : 7.00 Min. : 1.600 Min. : 1.200
## 1st Qu.: 5.350 1st Qu.:11.40 1st Qu.: 5.800 1st Qu.: 3.600
## Median : 7.200 Median :17.85 Median : 7.250 Median : 6.600
## Mean : 8.542 Mean :20.11 Mean : 7.683 Mean : 8.953
## 3rd Qu.:10.750 3rd Qu.:27.65 3rd Qu.: 9.350 3rd Qu.:14.500
## Max. :30.500 Max. :47.80 Max. :15.500 Max. :27.500
## NA's :10 NA's :15 NA's :15 NA's :24
## LifeExpectancy FemaleLabor Unemployment Energy
## Min. :52.20 Min. : 6.20 Min. : 0.100 Min. : 66
## 1st Qu.:66.90 1st Qu.:50.15 1st Qu.: 3.400 1st Qu.: 738
## Median :74.30 Median :60.60 Median : 5.600 Median : 1574
## Mean :72.46 Mean :57.95 Mean : 7.255 Mean : 2664
## 3rd Qu.:77.70 3rd Qu.:69.25 3rd Qu.: 9.400 3rd Qu.: 3060
## Max. :84.70 Max. :85.80 Max. :30.200 Max. :17923
## NA's :18 NA's :30 NA's :30 NA's :82
## Electricity Developed
## Min. : 39 Min. :1.00
## 1st Qu.: 904 1st Qu.:1.00
## Median : 2620 Median :2.00
## Mean : 4270 Mean :1.81
## 3rd Qu.: 5600 3rd Qu.:3.00
## Max. :53832 Max. :3.00
## NA's :76 NA's :75head(df)## # A tibble: 6 × 26
## Country Code LandArea Population Density GDP Rural CO2 PumpPrice Military
## <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Afghan… AFG 653. 37.2 56.9 521 74.5 0.29 0.7 3.72
## 2 Albania ALB 27.4 2.87 105. 5254 39.7 1.98 1.36 4.08
## 3 Algeria DZA 2382. 42.2 17.7 4279 27.4 3.74 0.28 13.8
## 4 Americ… ASM 0.2 0.055 277. NA 12.8 NA NA NA
## 5 Andorra AND 0.47 0.077 164. 42030 11.9 5.83 NA NA
## 6 Angola AGO 1247. 30.8 24.7 3432 34.5 1.29 0.97 9.4
## # ℹ 16 more variables: Health <dbl>, ArmedForces <dbl>, Internet <dbl>,
## # Cell <dbl>, HIV <dbl>, Hunger <dbl>, Diabetes <dbl>, BirthRate <dbl>,
## # DeathRate <dbl>, ElderlyPop <dbl>, LifeExpectancy <dbl>, FemaleLabor <dbl>,
## # Unemployment <dbl>, Energy <dbl>, Electricity <dbl>, Developed <dbl># Names of columns
names(df) ## [1] "Country" "Code" "LandArea" "Population"
## [5] "Density" "GDP" "Rural" "CO2"
## [9] "PumpPrice" "Military" "Health" "ArmedForces"
## [13] "Internet" "Cell" "HIV" "Hunger"
## [17] "Diabetes" "BirthRate" "DeathRate" "ElderlyPop"
## [21] "LifeExpectancy" "FemaleLabor" "Unemployment" "Energy"
## [25] "Electricity" "Developed"Handle missing values
# How many NA(s)
colSums(is.na(df)) ## Country Code LandArea Population Density
## 0 0 8 1 8
## GDP Rural CO2 PumpPrice Military
## 30 3 13 50 67
## Health ArmedForces Internet Cell HIV
## 29 49 13 15 81
## Hunger Diabetes BirthRate DeathRate ElderlyPop
## 52 10 15 15 24
## LifeExpectancy FemaleLabor Unemployment Energy Electricity
## 18 30 30 82 76
## Developed
## 75# Clean & filter: keep only numeric columns + identifiers
df_clean <- df |>
select(LifeExpectancy, GDP, Health, Internet) |>
mutate(across(where(is.numeric),
~ ifelse(is.na(.x), median(.x, na.rm = TRUE), .x)))
view(df_clean)Question 2
- Simple Linear Regression (Fitting and Interpretation): Using the AllCountries dataset, fit a simple linear regression model to predict LifeExpectancy (average life expectancy in years) based on GDP (gross domestic product per capita in $US). Report the intercept and slope coefficients and interpret their meaning in the context of the dataset. What does the R² value tell you about how well GDP explains variation in life expectancy across countries?
# Simple Linear Regression: LifeExpectancy -> GDP
simple_lm <- lm(LifeExpectancy ~ GDP, data = df_clean)
summary(simple_lm)##
## Call:
## lm(formula = LifeExpectancy ~ GDP, data = df_clean)
##
## Residuals:
## Min 1Q Median 3Q Max
## -17.453 -3.473 1.478 4.082 11.509
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.953e+01 4.996e-01 139.19 <2e-16 ***
## GDP 2.281e-04 2.134e-05 10.69 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.007 on 215 degrees of freedom
## Multiple R-squared: 0.3469, Adjusted R-squared: 0.3439
## F-statistic: 114.2 on 1 and 215 DF, p-value: < 2.2e-16Interpretation
The expected life expectancy would be roughly around the age 70(69.5) when all factors are omitted
When incorporating factors such as GDP in US dollars we see a slight increase in life expectancy as the slope rises at the rate of 0.00023 years
About 35% of the variation in life expectancy is explained by GDP. Suggesting a weak but meaningful relationship
Question 3
- Multiple Linear Regression (Fitting and Interpretation) Fit multiple linear regression model to predict LifeExpectancy using GDP, Health (percentage of government expenditures on healthcare), and Internet (percentage of population with internet access) as predictors. Interpret the coefficient for Health, explaining what it means in terms of life expectancy while controlling for GDP and Internet. How does the adjusted R² compare to the simple regression model from Question 1, and what does this suggest about the additional predictors?
# MULTIPLE REGRESSION
multiple_lm <- lm(LifeExpectancy ~ GDP + Health + Internet, data = df_clean)
summary(multiple_lm)##
## Call:
## lm(formula = LifeExpectancy ~ GDP + Health + Internet, data = df_clean)
##
## Residuals:
## Min 1Q Median 3Q Max
## -14.8409 -1.7949 0.4177 2.5649 9.1198
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.943e+01 7.417e-01 80.127 < 2e-16 ***
## GDP 2.637e-05 1.894e-05 1.392 0.165372
## Health 2.309e-01 5.888e-02 3.922 0.000119 ***
## Internet 1.905e-01 1.317e-02 14.466 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.017 on 213 degrees of freedom
## Multiple R-squared: 0.7106, Adjusted R-squared: 0.7065
## F-statistic: 174.3 on 3 and 213 DF, p-value: < 2.2e-16 adj_r2_mult <- summary(multiple_lm)$adj.r.squaredInterpretation
The expected life expectancy would be would increase by .23 years when incorporating the factor of government spending on residential health
Government funding on subsidies focused on the primary health of the citizens has an impact on the average life expectancy in a country.
About 71% of the variation in life expectancy is explained by GDP, Health, and Internet. Suggesting a strong and meaningful relationship
Question 4
- Checking Assumptions (Homoscedasticity and Normality) For the simple linear regression model from Question 1 (LifeExpectancy ~ GDP), describe how you would check the assumptions of homoscedasticity and normality of residuals. For each assumption, explain what an ideal outcome would look like and what a violation might indicate about the model’s reliability for predicting life expectancy. Afterwords, code your answer and reflect if it matched the ideal outcome.
Description
Using Homoscedasticity in which there is an assumption of equal variance within each group in this case countries allows for the presumption of little to no bias in the dataset.
- Ideal outcome
- The same vertical spread across fitted values
- vilations
- A cone shape or increasing spread
- Ideal outcome
Using Normality of Residuals in which there is an assumption that the dataset is normally distributed indicating that the dataset is in no shape or form skwed until evidently proven so with test that prove the observation are or are not normally distributed .
- Ideal outcome
- Points lie along the diagonal line
- vilations
- Curved pattern or extreme tail deviations
- Ideal outcome
# Homoscedasticity (constant variance)
plot(simple_lm, which = 1)
# Normality of Residuals
plot(simple_lm, which = 2) 
Reflection
Homoscedasticity was violated due to the concentration of the observations residing on the left side of the graph
The residuals are not perfectly normal indicating that the relationship might not be linear.
# Core diagnostics (covers: linearity, homoscedasticity, normality, influence)**
par(mfrow=c(2,2)); plot(simple_lm); par(mfrow=c(1,1))
Question 5
- Diagnosing Model Fit (RMSE and Residuals) For the multiple regression model from Question 2 (LifeExpectancy ~ GDP + Health + Internet), calculate the RMSE and explain what it represents in the context of predicting life expectancy. How would large residuals for certain countries (e.g., those with unusually high or low life expectancy) affect your confidence in the model’s predictions, and what might you investigate further?
# MODEL FIT: RMSE FOR MULTIPLE MODEL
residuals_mult <- resid(multiple_lm)
rmse_mult <- sqrt(mean(residuals_mult^2))
rmse_mult## [1] 3.980289Interpretation
- The life expectancy has a Root Mean Square of 4 years, meaning the life expectancy predction would be off by 4 years
Question 6
- Hypothetical Example (Multicollinearity in Multiple Regression) Suppose you are analyzing the AllCountries dataset and fit a multiple linear regression model to predict CO2 emissions (metric tons per capita) using Energy (kilotons of oil equivalent) and Electricity (kWh per capita) as predictors. You notice that Energy and Electricity are highly correlated. Explain how this multicollinearity might affect the interpretation of the regression coefficients and the reliability of the model.
# Hypothetical Multicollinearity –> CO2
lm(CO2 ~ Energy + Electricity, data = df)##
## Call:
## lm(formula = CO2 ~ Energy + Electricity, data = df)
##
## Coefficients:
## (Intercept) Energy Electricity
## 0.7998384 0.0031220 -0.0007044Explanation
- Multicollinearity makes the credibility of the predictors questionable. Although the model may still produce strong overall predictions, the highly correlated variables makes the coefficients less reliable and weakens confidence in how each predictor contributes to the outcome.