FA_LF_HW12
Folorunsho Atanda
2024-04-14
library(tidyverse)
library(data.table)data <- fread('https://raw.githubusercontent.com/folushoa/Data-Science/Data-605/HW12/who.csv')
print(head(data, 5))## Country LifeExp InfantSurvival Under5Survival TBFree PropMD
## <char> <int> <num> <num> <num> <num>
## 1: Afghanistan 42 0.835 0.743 0.99769 0.000228841
## 2: Albania 71 0.985 0.983 0.99974 0.001143127
## 3: Algeria 71 0.967 0.962 0.99944 0.001060478
## 4: Andorra 82 0.997 0.996 0.99983 0.003297297
## 5: Angola 41 0.846 0.740 0.99656 0.000070400
## PropRN PersExp GovtExp TotExp
## <num> <int> <int> <int>
## 1: 0.000572294 20 92 112
## 2: 0.004614439 169 3128 3297
## 3: 0.002091362 108 5184 5292
## 4: 0.003500000 2589 169725 172314
## 5: 0.001146162 36 1620 1656# Data dimension
dim(data)## [1] 190 10# Data structure
str(data)## Classes 'data.table' and 'data.frame': 190 obs. of 10 variables:
## $ Country : chr "Afghanistan" "Albania" "Algeria" "Andorra" ...
## $ LifeExp : int 42 71 71 82 41 73 75 69 82 80 ...
## $ InfantSurvival: num 0.835 0.985 0.967 0.997 0.846 0.99 0.986 0.979 0.995 0.996 ...
## $ Under5Survival: num 0.743 0.983 0.962 0.996 0.74 0.989 0.983 0.976 0.994 0.996 ...
## $ TBFree : num 0.998 1 0.999 1 0.997 ...
## $ PropMD : num 2.29e-04 1.14e-03 1.06e-03 3.30e-03 7.04e-05 ...
## $ PropRN : num 0.000572 0.004614 0.002091 0.0035 0.001146 ...
## $ PersExp : int 20 169 108 2589 36 503 484 88 3181 3788 ...
## $ GovtExp : int 92 3128 5184 169725 1620 12543 19170 1856 187616 189354 ...
## $ TotExp : int 112 3297 5292 172314 1656 13046 19654 1944 190797 193142 ...
## - attr(*, ".internal.selfref")=<externalptr># Statistical summary
summary(data)## Country LifeExp InfantSurvival Under5Survival
## Length:190 Min. :40.00 Min. :0.8350 Min. :0.7310
## Class :character 1st Qu.:61.25 1st Qu.:0.9433 1st Qu.:0.9253
## Mode :character Median :70.00 Median :0.9785 Median :0.9745
## Mean :67.38 Mean :0.9624 Mean :0.9459
## 3rd Qu.:75.00 3rd Qu.:0.9910 3rd Qu.:0.9900
## Max. :83.00 Max. :0.9980 Max. :0.9970
## TBFree PropMD PropRN PersExp
## Min. :0.9870 Min. :0.0000196 Min. :0.0000883 Min. : 3.00
## 1st Qu.:0.9969 1st Qu.:0.0002444 1st Qu.:0.0008455 1st Qu.: 36.25
## Median :0.9992 Median :0.0010474 Median :0.0027584 Median : 199.50
## Mean :0.9980 Mean :0.0017954 Mean :0.0041336 Mean : 742.00
## 3rd Qu.:0.9998 3rd Qu.:0.0024584 3rd Qu.:0.0057164 3rd Qu.: 515.25
## Max. :1.0000 Max. :0.0351290 Max. :0.0708387 Max. :6350.00
## GovtExp TotExp
## Min. : 10.0 Min. : 13
## 1st Qu.: 559.5 1st Qu.: 584
## Median : 5385.0 Median : 5541
## Mean : 40953.5 Mean : 41696
## 3rd Qu.: 25680.2 3rd Qu.: 26331
## Max. :476420.0 Max. :482750The attached who.csv dataset contains real-world data from 2008. The variables included follow.
Country: name of the country
LifeExp: average life expectancy for the country in years
InfantSurvival: proportion of those surviving to one year or more
Under5Survival: proportion of those surviving to five years or
more
TBFree: proportion of the population without TB.
PropMD: proportion of the population who are MDs
PropRN: proportion of the population who are RNs
PersExp: mean personal expenditures on healthcare in US dollars at
average exchange rate
GovtExp: mean government expenditures per capita on healthcare, US
dollars at average exchange rate
TotExp: sum of personal and government expenditures.
Question 1
Scatter Plot
data %>% ggplot(aes(x = TotExp, y = LifeExp)) +
geom_point() +
labs(title = 'Life Expectancy vs Total Expenditure',
x = 'Total Personal and Government Expenditure',
y = 'Life Expectancy (yrs)')
#### Linear Rigression
data_lm <- lm(LifeExp ~ TotExp, data = data)
summary(data_lm)##
## Call:
## lm(formula = LifeExp ~ TotExp, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -24.764 -4.778 3.154 7.116 13.292
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.475e+01 7.535e-01 85.933 < 2e-16 ***
## TotExp 6.297e-05 7.795e-06 8.079 7.71e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9.371 on 188 degrees of freedom
## Multiple R-squared: 0.2577, Adjusted R-squared: 0.2537
## F-statistic: 65.26 on 1 and 188 DF, p-value: 7.714e-14The F-statistic of the linear regression is 65.26.
This is significantly high, meaning that there is a significant
relationship between the two variables in the model.
The p-value is 7.71e-14, which is very low. This
indicates that in this model, TotExp is significantly
relevant to the model.
The multiple R-squared is 0.2577. This is saying that
the model only accounts for 25% of the variability of the life
expectancy can be explained by the total expenditure on healthcare. This
isn’t very high, which means that although there is a significant
relationship between the two variables, the total expenditure is not
enough to explain the variability in life expectancy.
The standard error is 9.371. Which means that using
this model 64% of the life expectancy falls between approximately ±9
years.
Question 2
Scatter Plot
Raise life expectancy to the 4.6 power (i.e., LifeExp^4.6). Raise total expenditures to the 0.06 power (nearly a log transform, TotExp^.06).
data$LifeExp <- data$LifeExp^4.6
data$TotExp <- data$TotExp^0.06
data %>% ggplot(aes(x = TotExp, y = LifeExp)) +
geom_point() +
labs(title = 'Life Expectancy vs Total Expenditure',
x = 'Total Personal and Government Expenditure',
y = 'Life Expectancy (yrs)')
#### Linear Rigression
data_lm <- lm(LifeExp ~ TotExp, data = data)
summary(data_lm)##
## Call:
## lm(formula = LifeExp ~ TotExp, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -308616089 -53978977 13697187 59139231 211951764
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -736527910 46817945 -15.73 <2e-16 ***
## TotExp 620060216 27518940 22.53 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 90490000 on 188 degrees of freedom
## Multiple R-squared: 0.7298, Adjusted R-squared: 0.7283
## F-statistic: 507.7 on 1 and 188 DF, p-value: < 2.2e-16The F-statistic of the linear regression is 507.7.
This is significantly high, meaning that there is a significant
relationship between the two variables in the model.
The p-value is 2.2e-16, which is very low. This
indicates that in this model, TotExp is significantly
relevant to the model.
The multiple R-squared is 0.7298. This is saying that
the model only accounts for 73% of the variability of the life
expectancy can be explained by the total expenditure on healthcare. This
is significantly high.
The standard error is 90490000. Which means that using
this model 64% of the life expectancy falls between approximately
±90490000 years.
Comparing the first model (model in question 1) and the second model (model in question 2), the model in the second model is better. This is because the value of the multiple R-square value and the standard error value from the second model is higher than the multiple R-square value and standard error value from the first model
Question 3
intercept <- -736527910
coefficient <- 620060216
# totExp_0.06 = 1.5
totExp_0.06 <- 1.5
forecast <- (intercept + coefficient * totExp_0.06)^(1/4.6)
paste("When total expenditure raised to the power 0.06 is 1.5, life expectancy is forecasted to be", forecast)## [1] "When total expenditure raised to the power 0.06 is 1.5, life expectancy is forecasted to be 63.3115334478635"# totExp_0.06 = 2.5
totExp_0.06 <- 2.5
forecast <- (intercept + coefficient * totExp_0.06)^(1/4.6)
paste("When total expenditure raised to the power 0.06 is 1.5, life expectancy is forecasted to be", forecast)## [1] "When total expenditure raised to the power 0.06 is 1.5, life expectancy is forecasted to be 86.5064484928337"Question 4
# original data
data <- fread('https://raw.githubusercontent.com/folushoa/Data-Science/Data-605/HW12/who.csv')
data_mlm <- lm(LifeExp ~ PropMD + TotExp + (PropMD * TotExp), data = data)
summary(data_mlm)##
## Call:
## lm(formula = LifeExp ~ PropMD + TotExp + (PropMD * TotExp), data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -27.320 -4.132 2.098 6.540 13.074
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.277e+01 7.956e-01 78.899 < 2e-16 ***
## PropMD 1.497e+03 2.788e+02 5.371 2.32e-07 ***
## TotExp 7.233e-05 8.982e-06 8.053 9.39e-14 ***
## PropMD:TotExp -6.026e-03 1.472e-03 -4.093 6.35e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.765 on 186 degrees of freedom
## Multiple R-squared: 0.3574, Adjusted R-squared: 0.3471
## F-statistic: 34.49 on 3 and 186 DF, p-value: < 2.2e-16The F-statistic of the linear regression is 34.49
with a F-statistic p-value of 2.2e-16. This indicates that there is a
significant relationship between the predictors and response variables
in the model, that is the probability that you would see these results
if the predictors had no effect is extremely low.
The p-value of the predictors are all very low; PropMD:
2.32e-07
TotExp: 9.39e-14
PropMD*TotExp: 6.35e-05
This indicates that in this model, that the predictors of this model are
all significantly relevant to the model.
The multiple R-squared is 0.3574. This is saying that
the model only accounts for 36% of the variability of the life
expectancy can be explained by the total expenditure on healthcare. This
is a moderate value.
The standard error is 8.765. Which means that using
this model 64% of the life expectancy falls between approximately ±9
years.
Based on the F-statistic, this model is only moderately good. The addition of more predictors might increase the effectiveness of the model.
Question 5
intercept <- 6.277e+01
coefficient_1 <- 1.497e+03
coefficient_2 <- 7.233e-05
coefficient_3 <- -6.026e-03
propMd <- 0.03
totExp <- 14
propMd_totExp <- propMd * totExp
forecast <- intercept + coefficient_1 * propMd + coefficient_2 * totExp + coefficient_3 * propMd_totExp
paste("When proportion of the population who are MDs is 0.03 and total expenditure is 14, life expectancy is forecasted to be", forecast)## [1] "When proportion of the population who are MDs is 0.03 and total expenditure is 14, life expectancy is forecasted to be 107.6784817"The life expectancy forecasted is ≈ 108 yrs. Although high this is
realistic. The oldest person alive in the U.S. is 114 years old.
Source: https://www.nbcnews.com/news/nbcblk/americas-oldest-living-person-114-may-also-fifth-oldest-person-earth-rcna141190