Scott Callahan — Dec 11, 2013, 11:57 AM
### Solutions for the various kinds of bad behavior in data:
# nonconstant error variance
# non-normal error distribution
# model using wrong predictors
# collinearity of predictors
ltrdata10 <- read.csv("~/Group_project-figure/ltrdata10.csv")
options(show.signif.stars=FALSE, digits=3)
ltrdata10$GDP <-log(ltrdata10$GDP)
ltrdata10$MOBILE <-log(ltrdata10$MOBILE)
View(ltrdata10)
row.names(ltrdata10) <- ltrdata10$Country.Name
ltrdata10$Country.Name <- NULL
ltrdata10$Region <- factor(ltrdata10$Region)
str(ltrdata10)
'data.frame': 95 obs. of 14 variables:
$ Country : Factor w/ 95 levels "Angola","Antigua and Barbuda",..: 1 2 3 4 5 6 7 8 9 10 ...
$ Region : Factor w/ 8 levels "AF","AS","AU",..: 1 4 8 5 4 6 2 5 1 8 ...
$ LTR : num 0.701 0.99 0.978 0.996 0.968 0.919 0.568 0.979 0.845 0.904 ...
$ GDP : num 8.35 9.47 9.12 8.05 10.1 ...
$ UNEMP : num 0.25 0.11 0.077 0.19 0.069 0.037 0.045 0.272 0.178 0.067 ...
$ SPGDP : num 0.035 0.025 0.058 0.032 0.069 0.029 0.022 0 0.078 0.058 ...
$ HTEXM : num 0 0 0.075 0.018 0.033 0.001 0.012 0.026 0.004 0.112 ...
$ HTEXD : num 0 0 1648290 3760 561 ...
$ URBGR : num 0.048 0.006 0.011 -0.002 0.003 0.05 0.027 0.008 0.021 0.012 ...
$ GINI : num 42.7 NA 44.5 31.3 NA ...
$ MOBILE : num 3.84 5.24 4.89 4.83 4.81 ...
$ INTERNET: num 10 80 45 25 62 ...
$ WMPOL : num 0.386 0.105 0.385 0.092 0 0.025 0.186 0.167 0.079 0.086 ...
$ LEXP : num 50.7 75.3 73.1 74.2 75 ...
levels(ltrdata10$Region) <- c("Africa", "Asia", "Oceanic", "C. America", "Europe","Mid. East", "N. America", "S. America")
summary(ltrdata10$Region)
Africa Asia Oceanic C. America Europe Mid. East
17 15 4 12 29 9
N. America S. America
3 6
## Locate all 0's in the data set and set them to NA
ltrdata10[ltrdata10 == 0] <- NA
summary (ltrdata10)
Country Region LTR GDP
Angola : 1 Europe :29 Min. :0.311 Min. : 5.35
Antigua and Barbuda: 1 Africa :17 1st Qu.:0.846 1st Qu.: 7.83
Argentina : 1 Asia :15 Median :0.947 Median : 8.80
Armenia : 1 C. America:12 Mean :0.887 Mean : 8.71
Aruba : 1 Mid. East : 9 3rd Qu.:0.990 3rd Qu.: 9.74
Bahrain : 1 S. America: 6 Max. :0.999 Max. :11.20
(Other) :89 (Other) : 7
UNEMP SPGDP HTEXM HTEXD
Min. :0.002 Min. :0.01 Min. :0.00 Min. :5.00e+01
1st Qu.:0.050 1st Qu.:0.03 1st Qu.:0.02 1st Qu.:9.62e+03
Median :0.084 Median :0.05 Median :0.06 Median :1.39e+05
Mean :0.111 Mean :0.05 Mean :0.09 Mean :1.82e+07
3rd Qu.:0.146 3rd Qu.:0.06 3rd Qu.:0.11 3rd Qu.:5.19e+06
Max. :0.512 Max. :0.11 Max. :0.50 Max. :4.06e+08
NA's :16 NA's :15 NA's :14
URBGR GINI MOBILE INTERNET
Min. :-0.0150 Min. :24.2 Min. :2.89 Min. : 0.2
1st Qu.: 0.0065 1st Qu.:32.8 1st Qu.:4.27 1st Qu.:11.6
Median : 0.0180 Median :37.6 Median :4.63 Median :31.6
Mean : 0.0205 Mean :40.0 Mean :4.49 Mean :36.8
3rd Qu.: 0.0300 3rd Qu.:45.7 3rd Qu.:4.82 3rd Qu.:55.6
Max. : 0.1150 Max. :65.0 Max. :5.24 Max. :90.7
NA's :6
WMPOL LEXP
Min. :0.00 Min. :46.4
1st Qu.:0.10 1st Qu.:67.1
Median :0.17 Median :73.5
Mean :0.19 Mean :70.9
3rd Qu.:0.24 3rd Qu.:76.6
Max. :0.45 Max. :82.8
NA's :6
## Checking for nonconstant variance of errors
g <- lm(LTR~GDP+UNEMP+ URBGR + MOBILE + LEXP , ltrdata10)
summary(g)
Call:
lm(formula = LTR ~ GDP + UNEMP + URBGR + MOBILE + LEXP, data = ltrdata10)
Residuals:
Min 1Q Median 3Q Max
-0.3358 -0.0402 0.0008 0.0334 0.2035
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.13939 0.11518 -1.21 0.22940
GDP 0.02100 0.01034 2.03 0.04531
UNEMP 0.24867 0.11122 2.24 0.02786
URBGR -1.21459 0.52967 -2.29 0.02420
MOBILE 0.10561 0.02619 4.03 0.00012
LEXP 0.00518 0.00167 3.11 0.00252
Residual standard error: 0.0883 on 89 degrees of freedom
Multiple R-squared: 0.66, Adjusted R-squared: 0.641
F-statistic: 34.6 on 5 and 89 DF, p-value: <2e-16
# Residual Plots
# Plot for detecting nonconstant variance and nonlinear departures from model
par(mfrow=c(1,1))
plot(fitted(g), residuals(g), xlab="Fitted", ylab="Residuals")
abline(h=0)
#Ceres Polt
library(car)
Warning: package 'car' was built under R version 3.0.2
ceresPlots(g, terms= ~ . - type)
# A better plot for detecting nonconstant variance
plot(fitted(g), abs(residuals(g)), xlab="Fitted", ylab="|Residuals|")
par(mfrow=c(1,1))
# An approximate test of noncontant variance
summary(lm(abs(residuals(g)) ~ fitted(g)))
Call:
lm(formula = abs(residuals(g)) ~ fitted(g))
Residuals:
Min 1Q Median 3Q Max
-0.0991 -0.0312 -0.0139 0.0226 0.2139
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.2887 0.0409 7.05 3.1e-10
fitted(g) -0.2578 0.0457 -5.64 1.8e-07
Residual standard error: 0.0531 on 93 degrees of freedom
Multiple R-squared: 0.255, Adjusted R-squared: 0.247
F-statistic: 31.8 on 1 and 93 DF, p-value: 1.85e-07
# Checking if nonconstant variance is related to a predictor
par(mfrow=c(1,1))
plot(ltrdata10$GDP, residuals(g), xlab="GDP", ylab="Residuals")
plot(ltrdata10$URBGR, residuals(g), xlab="Urban Growth", ylab="Residuals")
plot(ltrdata10$UNEMP, residuals(g), xlab="Unemployment", ylab="Residuals")
plot(ltrdata10$MOBILE, residuals(g), xlab="Mobile Subscribers", ylab="Residuals")
plot(ltrdata10$LEXP, residuals(g), xlab="Life Expectancy", ylab="Residuals")
par(mfrow=c(1,1))
# An F test for nonconstant error variance between two groups defined by a predictor
var.test(residuals(g)[ltrdata10$UNEMP>.05], residuals(g)[ltrdata10$UNEMP<.05])
F test to compare two variances
data: residuals(g)[ltrdata10$UNEMP > 0.05] and residuals(g)[ltrdata10$UNEMP < 0.05]
F = 0.548, num df = 69, denom df = 22, p-value = 0.06192
alternative hypothesis: true ratio of variances is not equal to 1
95 percent confidence interval:
0.258 1.030
sample estimates:
ratio of variances
0.548
var.test(residuals(g)[ltrdata10$GDP>8], residuals(g)[ltrdata10$GDP<8])
F test to compare two variances
data: residuals(g)[ltrdata10$GDP > 8] and residuals(g)[ltrdata10$GDP < 8]
F = 0.228, num df = 64, denom df = 29, p-value = 8.593e-07
alternative hypothesis: true ratio of variances is not equal to 1
95 percent confidence interval:
0.117 0.413
sample estimates:
ratio of variances
0.228
var.test(residuals(g)[ltrdata10$URBGR>.039], residuals(g)[ltrdata10$URBGR<.039])
F test to compare two variances
data: residuals(g)[ltrdata10$URBGR > 0.039] and residuals(g)[ltrdata10$URBGR < 0.039]
F = 2.32, num df = 12, denom df = 81, p-value = 0.02642
alternative hypothesis: true ratio of variances is not equal to 1
95 percent confidence interval:
1.10 6.54
sample estimates:
ratio of variances
2.32
var.test(residuals(g)[ltrdata10$MOBILE>4.5], residuals(g)[ltrdata10$MOBILE<4.5])
F test to compare two variances
data: residuals(g)[ltrdata10$MOBILE > 4.5] and residuals(g)[ltrdata10$MOBILE < 4.5]
F = 0.18, num df = 57, denom df = 36, p-value = 1.099e-08
alternative hypothesis: true ratio of variances is not equal to 1
95 percent confidence interval:
0.0971 0.3212
sample estimates:
ratio of variances
0.18
var.test(residuals(g)[ltrdata10$LEXP>65], residuals(g)[ltrdata10$LEXP<65])
F test to compare two variances
data: residuals(g)[ltrdata10$LEXP > 65] and residuals(g)[ltrdata10$LEXP < 65]
F = 0.387, num df = 75, denom df = 18, p-value = 0.004416
alternative hypothesis: true ratio of variances is not equal to 1
95 percent confidence interval:
0.169 0.749
sample estimates:
ratio of variances
0.387
# A variance stabilizing transformation
gg <- lm(LTR ~ GDP +UNEMP +URBGR + MOBILE + LEXP , ltrdata10)
gs <- lm((LTR)^2 ~ GDP +UNEMP+URBGR + MOBILE + LEXP , ltrdata10)
ge <- lm(log(LTR) ~ GDP +UNEMP+URBGR + MOBILE + LEXP , ltrdata10)
gr <- lm(sqrt(LTR) ~ GDP +UNEMP+URBGR + MOBILE + LEXP , ltrdata10)
par(mfrow=c(1,1))
plot(fitted(gg), residuals(gg), xlab="Fitted", ylab="Residuals")
plot(fitted(ge), residuals(ge), xlab="Fitted (Log)", ylab="Residuals")
plot(fitted(gr), residuals(gr), xlab="Fitted (Square-Root)", ylab="Residuals")
plot(fitted(gs), residuals(gs), xlab="Fitted (Squared)", ylab="Residuals")
spread.level.plot(g)
Warning: 'spread.level.plot' is deprecated. Use 'spreadLevelPlot' instead.
See help("Deprecated") and help("car-deprecated").
Suggested power transformation: 4.41
par(mfrow=c(1,1))
gB <- lm((LTR)^4.57~GDP+UNEMP+ URBGR + MOBILE + LEXP , ltrdata10)
summary(g); summary(gB)
Call:
lm(formula = (LTR)^4.57 ~ GDP + UNEMP + URBGR + MOBILE + LEXP,
data = ltrdata10)
Residuals:
Min 1Q Median 3Q Max
-0.4093 -0.1023 -0.0082 0.0841 0.5107
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -1.17186 0.24248 -4.83 5.6e-06
GDP 0.06025 0.02178 2.77 0.00688
UNEMP 0.29579 0.23414 1.26 0.20978
URBGR -4.20610 1.11509 -3.77 0.00029
MOBILE 0.16951 0.05513 3.07 0.00280
LEXP 0.00877 0.00351 2.50 0.01430
Residual standard error: 0.186 on 89 degrees of freedom
Multiple R-squared: 0.665, Adjusted R-squared: 0.646
F-statistic: 35.3 on 5 and 89 DF, p-value: <2e-16
plot(fitted(gB), residuals(gB), xlab="Fitted (Suggested)", ylab="Residuals")
abline(h=0)
a <- model.matrix(~LTR+GDP +UNEMP +URBGR + MOBILE + LEXP , ltrdata10)
cor(a)
Warning: the standard deviation is zero
(Intercept) LTR GDP UNEMP URBGR MOBILE LEXP
(Intercept) 1 NA NA NA NA NA NA
LTR NA 1.0000 0.676 -0.0766 -0.4710 0.700 0.681
GDP NA 0.6757 1.000 -0.1896 -0.2976 0.674 0.703
UNEMP NA -0.0766 -0.190 1.0000 -0.0577 -0.239 -0.380
URBGR NA -0.4710 -0.298 -0.0577 1.0000 -0.325 -0.403
MOBILE NA 0.7000 0.674 -0.2390 -0.3253 1.000 0.625
LEXP NA 0.6810 0.703 -0.3797 -0.4029 0.625 1.000
b <- model.matrix(~(LTR)^2 + GDP +UNEMP +URBGR + MOBILE + LEXP , ltrdata10)
cor(b)
Warning: the standard deviation is zero
(Intercept) LTR GDP UNEMP URBGR MOBILE LEXP
(Intercept) 1 NA NA NA NA NA NA
LTR NA 1.0000 0.676 -0.0766 -0.4710 0.700 0.681
GDP NA 0.6757 1.000 -0.1896 -0.2976 0.674 0.703
UNEMP NA -0.0766 -0.190 1.0000 -0.0577 -0.239 -0.380
URBGR NA -0.4710 -0.298 -0.0577 1.0000 -0.325 -0.403
MOBILE NA 0.7000 0.674 -0.2390 -0.3253 1.000 0.625
LEXP NA 0.6810 0.703 -0.3797 -0.4029 0.625 1.000
## Checking for non-normal errors
# QQ-plots for detecting nonnormality
par(mfrow=c(1,2))
qqnorm(residuals(g), ylab="Residuals")
qqline(residuals(g))
qqnorm(residuals(gB), ylab="Residuals")
qqline(residuals(gB))
# The histogram is not suitable for detecting nonnormality
par(mfrow=c(1,1))
hist(residuals(g))
#Non Constant Variance Test
ncvTest(g)
Non-constant Variance Score Test
Variance formula: ~ fitted.values
Chisquare = 43.1 Df = 1 p = 5.28e-11
#Much Lower F after correction
ncvTest(gB)
Non-constant Variance Score Test
Variance formula: ~ fitted.values
Chisquare = 6.81 Df = 1 p = 0.00906
# A test of normal versus nonnormal errors
shapiro.test(residuals(g))
Shapiro-Wilk normality test
data: residuals(g)
W = 0.944, p-value = 0.0005213
## Serial Correlation. Result: within lower and upper bounds, No serial correlation
dwtest(g)
Error: could not find function "dwtest"
## Checking for influential outliers
# The leverage measure for detecting influential outliers
library(faraway)
Attaching package: 'faraway'
The following object is masked from 'package:car':
logit, vif
par(mfrow=c(1,1))
countries <- ltrdata10$Country
halfnorm(lm.influence(g)$hat, labs=countries, ylab="Leverages")
#Q-Q Plot of the Studentized residuals
ginf<-influence(g)
gs<- summary(g)
gs$sig
[1] 0.0883
stud<- residuals(g)/(gs$sig*sqrt(1-ginf$hat))
qqnorm(stud)
abline(0,1)
ginf<-influence(gB)
gs<- summary(gB)
gs$sig
[1] 0.186
stud<- residuals(gB)/(gs$sig*sqrt(1-ginf$hat))
qqnorm(stud)
abline(0,1)
# These data have influential outliers visible with scatterplot
plot( ltrdata10$LTR,ltrdata10$GDP, xlab="Literacy Rates", ylab="GDP")
plot( ltrdata10$UNEMP,ltrdata10$GDP, xlab="Unemployment", ylab="GDP")
plot( ltrdata10$MOBILE,ltrdata10$GDP, xlab="Mobile Subscribers", ylab="GDP")
plot( ltrdata10$LEXP,ltrdata10$URBGR, xlab="Life Expectancy", ylab="Urban Growth Rate")
# The LS fitted line with outliers included in the data
gh <- lm(URBGR~ LEXP, ltrdata10)
abline(gh)
jack<- rstudent(gh,labs=countries)
jack[which.max(abs(jack))]
64
6.96
range(jack)
[1] -1.89 6.96
# The LS fitted line with outliers excluded from the data
ga <- lm(ltrdata10$URBGR~ ltrdata10$LEXP, subset=(ltrdata10$URBGR<.045))
abline(ga, lty=2)
gs <- lm(ltrdata10$URBGR~ ltrdata10$LEXP, subset=(ltrdata10$LEXP>60))
abline(gs, lty=5)
# Cook's Distance for detecting influential outliers
cook <- cooks.distance(g)
n<- length(cook)
sort(cook, partial=n-1)[n]
[1] 0.218
# Half normal plot of Cook's Distance with labels of three largest values
halfnorm(cook,3,labs=countries,ylab="Cook's distance")
plot(ginf$coef[,3],ylab="Change in Urban Growth")
plot(ginf$coef[,2],ylab="Change in Unemployment")
plot(ginf$coef[,1],ylab="Change in GDP")
# Model fit excluding observation with largest Cook's Distance
g1 <- lm(LTR ~ GDP +UNEMP +URBGR + MOBILE + LEXP , ltrdata10, subset=(cook < .15))
# Comparison of model fits with and without influential observation
coef(g); coef(g1); summary(g); summary(g1)
Call:
lm(formula = LTR ~ GDP + UNEMP + URBGR + MOBILE + LEXP, data = ltrdata10,
subset = (cook < 0.15))
Residuals:
Min 1Q Median 3Q Max
-0.18929 -0.03316 0.00579 0.02938 0.18359
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.00129 0.11014 -0.01 0.9907
GDP 0.01261 0.00918 1.37 0.1733
UNEMP 0.14492 0.09127 1.59 0.1161
URBGR -1.44412 0.54393 -2.65 0.0095
MOBILE 0.11976 0.02341 5.12 1.9e-06
LEXP 0.00362 0.00150 2.41 0.0180
Residual standard error: 0.071 on 84 degrees of freedom
Multiple R-squared: 0.695, Adjusted R-squared: 0.677
F-statistic: 38.3 on 5 and 84 DF, p-value: <2e-16
## Checking wrong predictors (model structure)
# Added varaible plot for checking model structure
d <- residuals(lm(LTR ~ GDP + UNEMP + URBGR + MOBILE , ltrdata10))
m <- residuals(lm(LEXP ~ GDP + UNEMP + URBGR + MOBILE , ltrdata10))
plot(m,d,xlab="Life Expectancy Residuals", ylab="Literacy Rates Residuals")
# The slope of the plot is the same as the coeficient in the full model
coef(lm(d~m)); coef(g); abline(0,coef(g)['LEXP'])
# Partial residual plot for checking model structure
plot(ltrdata10$LEXP, residuals(g)+coef(g)['LEXP']*ltrdata10$LEXP, xlab="Life Expectancy", ylab="Literacy Rates (Adjusted)")
abline(0,coef(g)['LEXP'])
# Easy wasy to get the added variable plot
library(faraway); prplot(g,5)
#Ceres Plot
library(car)
ceresPlots(g, terms= ~ . - type)
# Fitting and comparing model within two groups
g1 <- lm(LTR ~ GDP + UNEMP + URBGR + MOBILE + LEXP , ltrdata10, subset=(LEXP>63))
g2 <- lm(LTR ~ GDP + UNEMP + URBGR + MOBILE + LEXP , ltrdata10, subset=(LEXP<63))
summary(g1); summary(g2)
Call:
lm(formula = LTR ~ GDP + UNEMP + URBGR + MOBILE + LEXP, data = ltrdata10,
subset = (LEXP < 63))
Residuals:
Min 1Q Median 3Q Max
-0.2766 -0.0608 0.0275 0.0682 0.1785
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.53377 0.42985 -1.24 0.236
GDP 0.06115 0.04385 1.39 0.187
UNEMP 0.47605 0.22470 2.12 0.054
URBGR 0.32790 3.39236 0.10 0.924
MOBILE 0.08482 0.09667 0.88 0.396
LEXP 0.00624 0.00582 1.07 0.303
Residual standard error: 0.13 on 13 degrees of freedom
Multiple R-squared: 0.6, Adjusted R-squared: 0.447
F-statistic: 3.91 on 5 and 13 DF, p-value: 0.0221
## Checking for collinearity in predictors
# Signs of collinearity: The F test is highly significant and R-square is substantial, but none of the coefficents are significant
summary(g)
Call:
lm(formula = LTR ~ GDP + UNEMP + URBGR + MOBILE + LEXP, data = ltrdata10)
Residuals:
Min 1Q Median 3Q Max
-0.3358 -0.0402 0.0008 0.0334 0.2035
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.13939 0.11518 -1.21 0.22940
GDP 0.02100 0.01034 2.03 0.04531
UNEMP 0.24867 0.11122 2.24 0.02786
URBGR -1.21459 0.52967 -2.29 0.02420
MOBILE 0.10561 0.02619 4.03 0.00012
LEXP 0.00518 0.00167 3.11 0.00252
Residual standard error: 0.0883 on 89 degrees of freedom
Multiple R-squared: 0.66, Adjusted R-squared: 0.641
F-statistic: 34.6 on 5 and 89 DF, p-value: <2e-16
# The correlation matrix detects pairwise collinearity
# The Variance Inflation Factor (VIF)
library(faraway);
x <- model.matrix(g)[,-1]
vif(x)
GDP UNEMP URBGR MOBILE LEXP
2.45 1.27 1.29 2.03 2.69
round(cor(x),3)
GDP UNEMP URBGR MOBILE LEXP
GDP 1.000 -0.190 -0.298 0.674 0.703
UNEMP -0.190 1.000 -0.058 -0.239 -0.380
URBGR -0.298 -0.058 1.000 -0.325 -0.403
MOBILE 0.674 -0.239 -0.325 1.000 0.625
LEXP 0.703 -0.380 -0.403 0.625 1.000
# A solution: Amputate some predictors from the model
g2 <- lm(LTR ~ GDP + UNEMP+ URBGR + MOBILE, ltrdata10); summary(g2)
Call:
lm(formula = LTR ~ GDP + UNEMP + URBGR + MOBILE, data = ltrdata10)
Residuals:
Min 1Q Median 3Q Max
-0.3673 -0.0430 0.0064 0.0417 0.2295
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.04239 0.10390 0.41 0.68422
GDP 0.03681 0.00943 3.90 0.00018
UNEMP 0.11715 0.10769 1.09 0.27957
URBGR -1.74062 0.52552 -3.31 0.00133
MOBILE 0.12190 0.02686 4.54 1.8e-05
Residual standard error: 0.0924 on 90 degrees of freedom
Multiple R-squared: 0.623, Adjusted R-squared: 0.606
F-statistic: 37.2 on 4 and 90 DF, p-value: <2e-16
#####
# Generalized Least Squares
# When errors are not independent (Errors must be normal)
#first we look at all of our variables for correlation
plot(~LTR+GDP+UNEMP+URBGR+MOBILE+LEXP,ltrdata10)
cor(ltrdata10$LEXP,ltrdata10$GDP)
[1] 0.703
cor(ltrdata10$UNEMP,ltrdata10$GDP)
[1] -0.19
cor(ltrdata10$URBGR,ltrdata10$GDP)
[1] -0.298
cor(ltrdata10$MOBILE,ltrdata10$GDP) #
[1] 0.674
cor(ltrdata10$URBGR,ltrdata10$UNEMP) #
[1] -0.0577
cor(ltrdata10$MOBILE,ltrdata10$UNEMP)
[1] -0.239
cor(ltrdata10$LEXP,ltrdata10$UNEMP) #
[1] -0.38
cor(ltrdata10$MOBILE,ltrdata10$URBGR)
[1] -0.325
cor(ltrdata10$LEXP,ltrdata10$URBGR) #
[1] -0.403
cor(ltrdata10$LEXP,ltrdata10$MOBILE) #
[1] 0.625
#Strongest correlation is between GDP and Life Expectancy
#now look at summary of correlation of coeficients
m <- lm(LTR ~ GDP +UNEMP+ URBGR + MOBILE + LEXP , ltrdata10)
summary(m,cor=T)
Call:
lm(formula = LTR ~ GDP + UNEMP + URBGR + MOBILE + LEXP, data = ltrdata10)
Residuals:
Min 1Q Median 3Q Max
-0.3358 -0.0402 0.0008 0.0334 0.2035
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.13939 0.11518 -1.21 0.22940
GDP 0.02100 0.01034 2.03 0.04531
UNEMP 0.24867 0.11122 2.24 0.02786
URBGR -1.21459 0.52967 -2.29 0.02420
MOBILE 0.10561 0.02619 4.03 0.00012
LEXP 0.00518 0.00167 3.11 0.00252
Residual standard error: 0.0883 on 89 degrees of freedom
Multiple R-squared: 0.66, Adjusted R-squared: 0.641
F-statistic: 34.6 on 5 and 89 DF, p-value: <2e-16
Correlation of Coefficients:
(Intercept) GDP UNEMP URBGR MOBILE
GDP 0.18
UNEMP -0.50 -0.14
URBGR -0.53 -0.06 0.26
MOBILE -0.50 -0.43 0.09 0.12
LEXP -0.51 -0.49 0.38 0.32 -0.20
#correlation of GDP~LEXP is 0.703
#Correlation of coeficients is -0.49
#run two variables in gls model
cm <- gls(LTR~GDP + LEXP, correlation=corAR1(form= ~1), data=ltrdata10)
Error: could not find function "gls"
summary(cm)
Error: object of type 'closure' is not subsettable
intervals(cm)
Error: could not find function "intervals"
#phi value is 0.08 but not significant from 0(null Hypoth) in 95%CI
#no evidence of serial correlation
# Weighted Least Squares
# When the errors are uncorrelated but have nonconstant variance (Errors must be normal)
#Look at GDP as a predictor
plot(ltrdata10$GDP, residuals(g)); abline(h=0)
#variance much greater for low GDP countries
#quaity and reliability of data, globaization factors
#using model with weigts based on predictor GDP
#we want smaller weighted errors on smaller GDP contries
reg<- lm(LTR ~ GDP +UNEMP+ URBGR + MOBILE + LEXP,ltrdata10, weight=(1/GDP))
reg1 <- lm(LTR ~ GDP +UNEMP+ URBGR + MOBILE + LEXP,ltrdata10, weight=(1/sqrt(GDP)))
reg2 <- lm(LTR ~ GDP +UNEMP+ URBGR + MOBILE + LEXP,ltrdata10, weight=(35/GDP))
reg3 <- lm(LTR ~ GDP +UNEMP+ URBGR + MOBILE + LEXP,ltrdata10)
coef(reg)
(Intercept) GDP UNEMP URBGR MOBILE LEXP
-0.19678 0.01780 0.29215 -1.24424 0.11279 0.00587
coef(reg1)
(Intercept) GDP UNEMP URBGR MOBILE LEXP
-0.16838 0.01947 0.26975 -1.23212 0.10921 0.00552
coef(reg2)
(Intercept) GDP UNEMP URBGR MOBILE LEXP
-0.19678 0.01780 0.29215 -1.24424 0.11279 0.00587
coef(reg3)
(Intercept) GDP UNEMP URBGR MOBILE LEXP
-0.13939 0.02100 0.24867 -1.21459 0.10561 0.00518
#Test for Lack of Fit
plot(LTR ~ GDP, ltrdata10,xlab="GDP", ylab="Literacy Rates")
g <- lm(LTR ~ GDP, ltrdata10)
summary(g)
Call:
lm(formula = LTR ~ GDP, data = ltrdata10)
Residuals:
Min 1Q Median 3Q Max
-0.4176 -0.0507 0.0039 0.0617 0.2616
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.25845 0.07198 3.59 0.00053
GDP 0.07220 0.00817 8.84 5.8e-14
Residual standard error: 0.109 on 93 degrees of freedom
Multiple R-squared: 0.457, Adjusted R-squared: 0.451
F-statistic: 78.1 on 1 and 93 DF, p-value: 5.81e-14
abline(coef(g))
ga <- lm(LTR ~ GDP+UNEMP + URBGR + MOBILE + LEXP , ltrdata10)
summary(ga)$coef
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.13939 0.11518 -1.21 0.229404
GDP 0.02100 0.01034 2.03 0.045313
UNEMP 0.24867 0.11122 2.24 0.027860
URBGR -1.21459 0.52967 -2.29 0.024199
MOBILE 0.10561 0.02619 4.03 0.000116
LEXP 0.00518 0.00167 3.11 0.002525
summary(ga)$sigma
[1] 0.0883
summary(ga)$r.squared
[1] 0.66
summary(ga)
Call:
lm(formula = LTR ~ GDP + UNEMP + URBGR + MOBILE + LEXP, data = ltrdata10)
Residuals:
Min 1Q Median 3Q Max
-0.3358 -0.0402 0.0008 0.0334 0.2035
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.13939 0.11518 -1.21 0.22940
GDP 0.02100 0.01034 2.03 0.04531
UNEMP 0.24867 0.11122 2.24 0.02786
URBGR -1.21459 0.52967 -2.29 0.02420
MOBILE 0.10561 0.02619 4.03 0.00012
LEXP 0.00518 0.00167 3.11 0.00252
Residual standard error: 0.0883 on 89 degrees of freedom
Multiple R-squared: 0.66, Adjusted R-squared: 0.641
F-statistic: 34.6 on 5 and 89 DF, p-value: <2e-16
points(ltrdata10$GDP,fitted(ga), pch=18)
anova(g,ga)
Analysis of Variance Table
Model 1: LTR ~ GDP
Model 2: LTR ~ GDP + UNEMP + URBGR + MOBILE + LEXP
Res.Df RSS Df Sum of Sq F Pr(>F)
1 93 1.109
2 89 0.694 4 0.415 13.3 1.5e-08
gt<- lm(LTR~ GDP + I(GDP^2), ltrdata10)
summary(gt)
Call:
lm(formula = LTR ~ GDP + I(GDP^2), data = ltrdata10)
Residuals:
Min 1Q Median 3Q Max
-0.3711 -0.0417 0.0095 0.0398 0.3007
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -1.15545 0.36855 -3.14 0.00231
GDP 0.41067 0.08709 4.72 8.5e-06
I(GDP^2) -0.01973 0.00506 -3.90 0.00018
Residual standard error: 0.102 on 92 degrees of freedom
Multiple R-squared: 0.534, Adjusted R-squared: 0.524
F-statistic: 52.7 on 2 and 92 DF, p-value: 5.7e-16
plot(LTR ~ GDP, ltrdata10)
grid <- seq(6,11)
lines(grid,predict(gt,data.frame(GDP=grid)))
points(ltrdata10$GDP,fitted(ga), pch=18)
#####
#Robust Regression
######
#Discusses possibility of outliers that distort OLS estimates
library(faraway);# data(gala)
g1 <- lm(LTR ~ GDP+ UNEMP+ URBGR + MOBILE + LEXP + INTERNET, ltrdata10)
summary(g1)$coef
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.213502 0.154620 -1.381 0.170833
GDP 0.027137 0.013418 2.022 0.046164
UNEMP 0.261146 0.112855 2.314 0.022997
URBGR -1.202859 0.531359 -2.264 0.026049
MOBILE 0.105745 0.026259 4.027 0.000119
LEXP 0.005707 0.001824 3.129 0.002378
INTERNET -0.000513 0.000712 -0.721 0.472901
qqnorm(residuals(g1))
qqline(residuals(g1))
shapiro.test(residuals(g1))
Shapiro-Wilk normality test
data: residuals(g1)
W = 0.951, p-value = 0.001438
#######
#Demonstrates how outliers distort OLS estimates
row.names(ltrdata10) <- ltrdata10$Country
Country <- row.names(ltrdata10)
halfnorm(cooks.distance(g1), 3, labs=Country, ylab="Cook's distance")
plot(influence(g1)$coef[,3], ylab="Change in GDP coef")
#identify(1:95, influence(g1)$coef[,3], Country)
#######
##Compares OLS, Huber, LAD, and LTS methods
# Huber M-estimation
library(MASS)
gr <- rlm(LTR ~ GDP+ UNEMP+ URBGR + MOBILE + LEXP + INTERNET, ltrdata10)
summary(gr)$coef
Value Std. Error t value
(Intercept) -0.086505 0.12159 -0.711
GDP 0.016922 0.01055 1.604
UNEMP 0.239187 0.08875 2.695
URBGR -0.906616 0.41785 -2.170
MOBILE 0.112367 0.02065 5.442
LEXP 0.004361 0.00143 3.041
INTERNET 0.000163 0.00056 0.292
# Least Absolution Deviation (LAD)
library(quantreg)
Warning: package 'quantreg' was built under R version 3.0.2
Loading required package: SparseM
Attaching package: 'SparseM'
The following object is masked from 'package:base':
backsolve
gq <- rq(LTR ~ GDP+ UNEMP+ URBGR + MOBILE + LEXP + INTERNET,data= ltrdata10)
summary(gq)$coef
coefficients lower bd upper bd
(Intercept) 0.070280 -0.384483 0.26503
GDP 0.003726 -0.009509 0.03775
UNEMP 0.122185 0.066406 0.52169
URBGR -1.235583 -2.643607 -0.16531
MOBILE 0.122512 0.050372 0.15269
LEXP 0.003441 0.001638 0.00775
INTERNET 0.000316 -0.000945 0.00118
# Least Trimmed Squares (LTS)
library(robustbase)
Warning: package 'robustbase' was built under R version 3.0.2
Attaching package: 'robustbase'
The following object is masked from 'package:faraway':
epilepsy
ltsReg(LTR ~ GDP+ UNEMP+ URBGR + MOBILE + LEXP + INTERNET, ltrdata10)$coef
Intercept GDP UNEMP URBGR MOBILE LEXP INTERNET
1.161353 -0.006331 -0.125576 -1.365099 -0.011149 -0.001211 0.000819
ltsReg(LTR ~ GDP+ UNEMP+ URBGR + MOBILE + LEXP + INTERNET, ltrdata10, nsamp="95")$coef
Intercept GDP UNEMP URBGR MOBILE LEXP INTERNET
1.161353 -0.006331 -0.125576 -1.365099 -0.011149 -0.001211 0.000819
# Comparison of Huber, LAD, LTS
plot(LTR ~ GDP, ltrdata10)
abline(lm(LTR ~ GDP, ltrdata10)$coef) # LS
abline(rlm(LTR ~ GDP, ltrdata10)$coef, lty=2) # Huber
abline(rq(ltrdata10$LTR ~ ltrdata10$GDP)$coef, lty=5) # LAD
abline(ltsreg(LTR ~ GDP, ltrdata10)$coef, lty=7) # LTS
# Print estimated coefficients and their standard errors in a table for several regression models
library(car)
library(faraway)
library(MASS)
#data()
gLS <- lm(LTR ~ GDP, ltrdata10)
gHub <- rlm(LTR ~ GDP, ltrdata10)
compareCoefs(gLS, gHub)
Call:
1:"lm(formula = LTR ~ GDP, data = ltrdata10)"
2:"rlm(formula = LTR ~ GDP, data = ltrdata10)"
Est. 1 SE 1 Est. 2 SE 2
(Intercept) 0.25845 0.07198 0.34193 0.06404
GDP 0.07220 0.00817 0.06343 0.00727
#############
##ITEM7
#Shows role of ANOVA test of Big vs. Small Model
fit <- lm(LTR ~ GDP+ UNEMP+ URBGR + MOBILE + LEXP + INTERNET , data = ltrdata10)
summary(fit)
Call:
lm(formula = LTR ~ GDP + UNEMP + URBGR + MOBILE + LEXP + INTERNET,
data = ltrdata10)
Residuals:
Min 1Q Median 3Q Max
-0.3312 -0.0421 -0.0003 0.0307 0.2069
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.213502 0.154620 -1.38 0.17083
GDP 0.027137 0.013418 2.02 0.04616
UNEMP 0.261146 0.112855 2.31 0.02300
URBGR -1.202859 0.531359 -2.26 0.02605
MOBILE 0.105745 0.026259 4.03 0.00012
LEXP 0.005707 0.001824 3.13 0.00238
INTERNET -0.000513 0.000712 -0.72 0.47290
Residual standard error: 0.0885 on 88 degrees of freedom
Multiple R-squared: 0.662, Adjusted R-squared: 0.639
F-statistic: 28.7 on 6 and 88 DF, p-value: <2e-16
fit2 <- lm(LTR ~ GDP + UNEMP + URBGR + MOBILE + LEXP, ltrdata10)
summary(fit2)
Call:
lm(formula = LTR ~ GDP + UNEMP + URBGR + MOBILE + LEXP, data = ltrdata10)
Residuals:
Min 1Q Median 3Q Max
-0.3358 -0.0402 0.0008 0.0334 0.2035
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.13939 0.11518 -1.21 0.22940
GDP 0.02100 0.01034 2.03 0.04531
UNEMP 0.24867 0.11122 2.24 0.02786
URBGR -1.21459 0.52967 -2.29 0.02420
MOBILE 0.10561 0.02619 4.03 0.00012
LEXP 0.00518 0.00167 3.11 0.00252
Residual standard error: 0.0883 on 89 degrees of freedom
Multiple R-squared: 0.66, Adjusted R-squared: 0.641
F-statistic: 34.6 on 5 and 89 DF, p-value: <2e-16
anova(fit2,fit)
Analysis of Variance Table
Model 1: LTR ~ GDP + UNEMP + URBGR + MOBILE + LEXP
Model 2: LTR ~ GDP + UNEMP + URBGR + MOBILE + LEXP + INTERNET
Res.Df RSS Df Sum of Sq F Pr(>F)
1 89 0.694
2 88 0.689 1 0.00407 0.52 0.47
fit3 <- lm(LTR ~ UNEMP+ URBGR + MOBILE + LEXP + INTERNET, ltrdata10)
summary(fit3)
Call:
lm(formula = LTR ~ UNEMP + URBGR + MOBILE + LEXP + INTERNET,
data = ltrdata10)
Residuals:
Min 1Q Median 3Q Max
-0.3432 -0.0449 0.0041 0.0360 0.2244
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.114051 0.149116 -0.76 0.4464
UNEMP 0.263512 0.114791 2.30 0.0240
URBGR -1.175200 0.540327 -2.17 0.0323
MOBILE 0.123083 0.025247 4.88 4.7e-06
LEXP 0.006054 0.001847 3.28 0.0015
INTERNET 0.000400 0.000559 0.72 0.4764
Residual standard error: 0.09 on 89 degrees of freedom
Multiple R-squared: 0.646, Adjusted R-squared: 0.626
F-statistic: 32.5 on 5 and 89 DF, p-value: <2e-16
anova(fit3,fit)
Analysis of Variance Table
Model 1: LTR ~ UNEMP + URBGR + MOBILE + LEXP + INTERNET
Model 2: LTR ~ GDP + UNEMP + URBGR + MOBILE + LEXP + INTERNET
Res.Df RSS Df Sum of Sq F Pr(>F)
1 89 0.722
2 88 0.689 1 0.032 4.09 0.046
#####
##Demonstrates backward variable selection manually
g <- lm(LTR ~ GDP+UNEMP+URBGR+MOBILE+INTERNET+LEXP+GINI, data=ltrdata10)
summary(g)
Call:
lm(formula = LTR ~ GDP + UNEMP + URBGR + MOBILE + INTERNET +
LEXP + GINI, data = ltrdata10)
Residuals:
Min 1Q Median 3Q Max
-0.3221 -0.0406 0.0013 0.0384 0.2087
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.233208 0.158564 -1.47 0.145
GDP 0.017096 0.015235 1.12 0.265
UNEMP 0.201159 0.117983 1.70 0.092
URBGR -1.177464 0.550982 -2.14 0.036
MOBILE 0.125477 0.029899 4.20 6.9e-05
INTERNET 0.000178 0.000831 0.21 0.831
LEXP 0.004956 0.001972 2.51 0.014
GINI 0.001287 0.001198 1.07 0.286
Residual standard error: 0.0886 on 81 degrees of freedom
(6 observations deleted due to missingness)
Multiple R-squared: 0.683, Adjusted R-squared: 0.656
F-statistic: 24.9 on 7 and 81 DF, p-value: <2e-16
# Illustration of the Backward Method
g <- update(g, . ~ . - INTERNET)
summary(g)
Call:
lm(formula = LTR ~ GDP + UNEMP + URBGR + MOBILE + LEXP + GINI,
data = ltrdata10)
Residuals:
Min 1Q Median 3Q Max
-0.3216 -0.0419 0.0021 0.0393 0.2079
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.25237 0.13014 -1.94 0.0559
GDP 0.01942 0.01062 1.83 0.0710
UNEMP 0.20716 0.11394 1.82 0.0727
URBGR -1.17178 0.54713 -2.14 0.0352
MOBILE 0.12468 0.02949 4.23 6.1e-05
LEXP 0.00512 0.00180 2.84 0.0056
GINI 0.00120 0.00112 1.07 0.2878
Residual standard error: 0.088 on 82 degrees of freedom
(6 observations deleted due to missingness)
Multiple R-squared: 0.683, Adjusted R-squared: 0.66
F-statistic: 29.4 on 6 and 82 DF, p-value: <2e-16
g <- update(g, . ~ . - GINI)
summary(g)
Call:
lm(formula = LTR ~ GDP + UNEMP + URBGR + MOBILE + LEXP, data = ltrdata10)
Residuals:
Min 1Q Median 3Q Max
-0.3358 -0.0402 0.0008 0.0334 0.2035
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.13939 0.11518 -1.21 0.22940
GDP 0.02100 0.01034 2.03 0.04531
UNEMP 0.24867 0.11122 2.24 0.02786
URBGR -1.21459 0.52967 -2.29 0.02420
MOBILE 0.10561 0.02619 4.03 0.00012
LEXP 0.00518 0.00167 3.11 0.00252
Residual standard error: 0.0883 on 89 degrees of freedom
Multiple R-squared: 0.66, Adjusted R-squared: 0.641
F-statistic: 34.6 on 5 and 89 DF, p-value: <2e-16
g <- update(g, . ~ . - UNEMP)
summary(g)
Call:
lm(formula = LTR ~ GDP + URBGR + MOBILE + LEXP, data = ltrdata10)
Residuals:
Min 1Q Median 3Q Max
-0.3528 -0.0400 0.0061 0.0371 0.2073
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.01084 0.10200 -0.11 0.91562
GDP 0.02426 0.01047 2.32 0.02272
URBGR -1.51737 0.52332 -2.90 0.00470
MOBILE 0.10056 0.02666 3.77 0.00029
LEXP 0.00376 0.00158 2.39 0.01898
Residual standard error: 0.0902 on 90 degrees of freedom
Multiple R-squared: 0.641, Adjusted R-squared: 0.625
F-statistic: 40.2 on 4 and 90 DF, p-value: <2e-16
######
###Effectively uses stepwise regression to obtain a model
g <- lm(LTR ~ GDP+UNEMP+URBGR+MOBILE+INTERNET+LEXP, data = ltrdata10)
step(g)
Start: AIC=-454
LTR ~ GDP + UNEMP + URBGR + MOBILE + INTERNET + LEXP
Df Sum of Sq RSS AIC
- INTERNET 1 0.0041 0.694 -455
<none> 0.689 -454
- GDP 1 0.0320 0.722 -452
- URBGR 1 0.0402 0.730 -451
- UNEMP 1 0.0420 0.731 -450
- LEXP 1 0.0767 0.766 -446
- MOBILE 1 0.1271 0.817 -440
Step: AIC=-455
LTR ~ GDP + UNEMP + URBGR + MOBILE + LEXP
Df Sum of Sq RSS AIC
<none> 0.694 -455
- GDP 1 0.0321 0.726 -453
- UNEMP 1 0.0390 0.733 -452
- URBGR 1 0.0410 0.735 -452
- LEXP 1 0.0753 0.769 -448
- MOBILE 1 0.1267 0.820 -441
Call:
lm(formula = LTR ~ GDP + UNEMP + URBGR + MOBILE + LEXP, data = ltrdata10)
Coefficients:
(Intercept) GDP UNEMP URBGR MOBILE
-0.13939 0.02100 0.24867 -1.21459 0.10561
LEXP
0.00518
# Criterion-Based Procedures
# Akaike Information Criterion nlog(SSE/n)+constant
g <- lm(LTR ~ GDP+UNEMP+URBGR+MOBILE+LEXP+INTERNET, data = ltrdata10)
step(g)
Start: AIC=-454
LTR ~ GDP + UNEMP + URBGR + MOBILE + LEXP + INTERNET
Df Sum of Sq RSS AIC
- INTERNET 1 0.0041 0.694 -455
<none> 0.689 -454
- GDP 1 0.0320 0.722 -452
- URBGR 1 0.0402 0.730 -451
- UNEMP 1 0.0420 0.731 -450
- LEXP 1 0.0767 0.766 -446
- MOBILE 1 0.1271 0.817 -440
Step: AIC=-455
LTR ~ GDP + UNEMP + URBGR + MOBILE + LEXP
Df Sum of Sq RSS AIC
<none> 0.694 -455
- GDP 1 0.0321 0.726 -453
- UNEMP 1 0.0390 0.733 -452
- URBGR 1 0.0410 0.735 -452
- LEXP 1 0.0753 0.769 -448
- MOBILE 1 0.1267 0.820 -441
Call:
lm(formula = LTR ~ GDP + UNEMP + URBGR + MOBILE + LEXP, data = ltrdata10)
Coefficients:
(Intercept) GDP UNEMP URBGR MOBILE
-0.13939 0.02100 0.24867 -1.21459 0.10561
LEXP
0.00518
# Influential points can have an effect on selected model
h <- lm.influence(g)$hat
Country <- row.names(ltrdata10)
rev(sort(h))
Qatar Congo, Dem. Rep. Namibia
0.3979 0.2982 0.2808
United Arab Emirates Botswana Samoa
0.2576 0.2361 0.2353
Equatorial Guinea Kenya Chad
0.2260 0.1616 0.1199
Mozambique Angola Uganda
0.1167 0.1155 0.1088
South Africa Macedonia, FYR Papua New Guinea
0.1082 0.1081 0.1071
Vietnam Antigua and Barbuda Nigeria
0.1022 0.0992 0.0989
Nepal Gabon Turkmenistan
0.0977 0.0959 0.0834
Bosnia and Herzegovina Canada Puerto Rico
0.0820 0.0783 0.0780
Lithuania Montenegro Netherlands
0.0735 0.0724 0.0707
Mali Honduras Bangladesh
0.0704 0.0701 0.0694
Iraq Tajikistan Latvia
0.0692 0.0684 0.0674
Tanzania Armenia Timor-Leste
0.0666 0.0648 0.0647
Guatemala Sweden Panama
0.0638 0.0618 0.0612
Bahrain Russian Federation Estonia
0.0588 0.0588 0.0576
Greece France Zambia
0.0571 0.0562 0.0561
Japan Switzerland Spain
0.0560 0.0558 0.0557
Finland Costa Rica Vanuatu
0.0551 0.0547 0.0538
United States Germany Syrian Arab Republic
0.0532 0.0532 0.0514
United Kingdom Saudi Arabia Sri Lanka
0.0505 0.0500 0.0499
Suriname Uzbekistan Ukraine
0.0494 0.0486 0.0477
Moldova El Salvador Italy
0.0470 0.0448 0.0434
Cyprus Serbia Brunei Darussalam
0.0413 0.0407 0.0403
Sudan Trinidad and Tobago Kazakhstan
0.0399 0.0395 0.0391
Mexico Slovenia Mongolia
0.0377 0.0376 0.0375
Georgia India Singapore
0.0374 0.0374 0.0370
China Ghana Hungary
0.0367 0.0365 0.0361
Yemen, Rep. Aruba Malaysia
0.0356 0.0351 0.0349
Poland Jamaica Romania
0.0344 0.0325 0.0302
Ecuador Jordan Paraguay
0.0299 0.0286 0.0279
Portugal Croatia Uruguay
0.0257 0.0237 0.0230
Argentina Egypt, Arab Rep. Brazil
0.0220 0.0196 0.0194
Dominican Republic Colombia
0.0167 0.0133
# Qatar has high leverage, try removing it
g <- lm(LTR ~ GDP+UNEMP+URBGR+MOBILE+INTERNET+LEXP, data = ltrdata10, subset=(Country != "Qatar"))
step(g)
Start: AIC=-450
LTR ~ GDP + UNEMP + URBGR + MOBILE + INTERNET + LEXP
Df Sum of Sq RSS AIC
- INTERNET 1 0.0054 0.680 -451
<none> 0.674 -450
- GDP 1 0.0268 0.701 -448
- UNEMP 1 0.0406 0.715 -447
- URBGR 1 0.0550 0.729 -445
- LEXP 1 0.0701 0.744 -443
- MOBILE 1 0.1266 0.801 -436
Step: AIC=-451
LTR ~ GDP + UNEMP + URBGR + MOBILE + LEXP
Df Sum of Sq RSS AIC
<none> 0.680 -451
- GDP 1 0.0227 0.702 -450
- UNEMP 1 0.0371 0.717 -448
- URBGR 1 0.0542 0.734 -446
- LEXP 1 0.0657 0.745 -445
- MOBILE 1 0.1262 0.806 -437
Call:
lm(formula = LTR ~ GDP + UNEMP + URBGR + MOBILE + LEXP, data = ltrdata10,
subset = (Country != "Qatar"))
Coefficients:
(Intercept) GDP UNEMP URBGR MOBILE
-0.08193 0.01805 0.24276 -1.73291 0.10540
LEXP
0.00488
# Transforming variables can have an effect
ltrdata10$Country<-NULL
ltrdata10$Region<-NULL
stripchart (data.frame (scale (ltrdata10)), vertical=TRUE,method="jitter")
g <- lm(LTR ~ GDP+ log(UNEMP)+ URBGR+ MOBILE+LEXP+INTERNET, data = ltrdata10)
step(g)
Start: AIC=-449
LTR ~ GDP + log(UNEMP) + URBGR + MOBILE + LEXP + INTERNET
Df Sum of Sq RSS AIC
- INTERNET 1 0.0007 0.731 -450
- log(UNEMP) 1 0.0016 0.731 -450
<none> 0.730 -449
- LEXP 1 0.0305 0.760 -447
- GDP 1 0.0334 0.763 -446
- URBGR 1 0.0645 0.794 -442
- MOBILE 1 0.1143 0.844 -437
Step: AIC=-450
LTR ~ GDP + log(UNEMP) + URBGR + MOBILE + LEXP
Df Sum of Sq RSS AIC
- log(UNEMP) 1 0.0020 0.733 -452
<none> 0.731 -450
- LEXP 1 0.0321 0.763 -448
- GDP 1 0.0457 0.776 -447
- URBGR 1 0.0654 0.796 -444
- MOBILE 1 0.1143 0.845 -439
Step: AIC=-452
LTR ~ GDP + URBGR + MOBILE + LEXP
Df Sum of Sq RSS AIC
<none> 0.733 -452
- GDP 1 0.0437 0.776 -449
- LEXP 1 0.0465 0.779 -448
- URBGR 1 0.0684 0.801 -446
- MOBILE 1 0.1158 0.848 -440
Call:
lm(formula = LTR ~ GDP + URBGR + MOBILE + LEXP, data = ltrdata10)
Coefficients:
(Intercept) GDP URBGR MOBILE LEXP
-0.01084 0.02426 -1.51737 0.10056 0.00376
#####
# Cross-Validation for Linear Models
##Explains the usage of training and valitation dataset
g <- lm(LTR ~ GDP+UNEMP+URBGR+MOBILE+INTERNET+LEXP, data = ltrdata10)
g.step <- step(g)
Start: AIC=-454
LTR ~ GDP + UNEMP + URBGR + MOBILE + INTERNET + LEXP
Df Sum of Sq RSS AIC
- INTERNET 1 0.0041 0.694 -455
<none> 0.689 -454
- GDP 1 0.0320 0.722 -452
- URBGR 1 0.0402 0.730 -451
- UNEMP 1 0.0420 0.731 -450
- LEXP 1 0.0767 0.766 -446
- MOBILE 1 0.1271 0.817 -440
Step: AIC=-455
LTR ~ GDP + UNEMP + URBGR + MOBILE + LEXP
Df Sum of Sq RSS AIC
<none> 0.694 -455
- GDP 1 0.0321 0.726 -453
- UNEMP 1 0.0390 0.733 -452
- URBGR 1 0.0410 0.735 -452
- LEXP 1 0.0753 0.769 -448
- MOBILE 1 0.1267 0.820 -441
summary(g.step)
Call:
lm(formula = LTR ~ GDP + UNEMP + URBGR + MOBILE + LEXP, data = ltrdata10)
Residuals:
Min 1Q Median 3Q Max
-0.3358 -0.0402 0.0008 0.0334 0.2035
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.13939 0.11518 -1.21 0.22940
GDP 0.02100 0.01034 2.03 0.04531
UNEMP 0.24867 0.11122 2.24 0.02786
URBGR -1.21459 0.52967 -2.29 0.02420
MOBILE 0.10561 0.02619 4.03 0.00012
LEXP 0.00518 0.00167 3.11 0.00252
Residual standard error: 0.0883 on 89 degrees of freedom
Multiple R-squared: 0.66, Adjusted R-squared: 0.641
F-statistic: 34.6 on 5 and 89 DF, p-value: <2e-16
library(DAAG)
Warning: package 'DAAG' was built under R version 3.0.2
Loading required package: lattice
Attaching package: 'lattice'
The following object is masked from 'package:faraway':
melanoma
Attaching package: 'DAAG'
The following object is masked from 'package:robustbase':
milk
The following object is masked from 'package:MASS':
hills
The following object is masked from 'package:faraway':
orings, ozone, vif
The following object is masked from 'package:car':
vif
# Crossvalidation of model as a portion or "fold" is held out, default is 3 folds
par(mfrow=c(1,2))
CVlm(df=ltrdata10, form.lm=g.step)
Analysis of Variance Table
Response: LTR
Df Sum Sq Mean Sq F value Pr(>F)
GDP 1 0.932 0.932 119.54 < 2e-16
UNEMP 1 0.006 0.006 0.72 0.3989
URBGR 1 0.158 0.158 20.30 2.0e-05
MOBILE 1 0.176 0.176 22.57 7.7e-06
LEXP 1 0.075 0.075 9.66 0.0025
Residuals 89 0.694 0.008
Warning:
As there is >1 explanatory variable, cross-validation predicted values for
a fold are not a linear function of corresponding overall predicted
values. Lines that are shown for the different folds are approximate
fold 1
Observations in test set: 31
Armenia Aruba Bahrain Brazil Brunei Darussalam Colombia
Predicted 0.9737 0.9823 0.9195 0.937 0.95844 0.9131
cvpred 0.9846 0.9843 0.8971 0.933 0.94968 0.9101
LTR 0.9960 0.9680 0.9190 0.904 0.95200 0.9340
CV residual 0.0114 -0.0163 0.0219 -0.029 0.00232 0.0239
El Salvador Estonia Germany Ghana Greece India Jordan
Predicted 0.9125 1.0012 1.028 0.7515 1.0101 0.7678 0.9113
cvpred 0.9005 1.0152 1.035 0.7282 1.0209 0.7453 0.9046
LTR 0.8450 0.9980 0.990 0.6730 0.9720 0.7400 0.9260
CV residual -0.0555 -0.0172 -0.045 -0.0552 -0.0489 -0.0053 0.0214
Latvia Malaysia Mexico Namibia Panama Papua New Guinea
Predicted 0.98123 0.9140 0.9056 0.9229 0.9819 0.6694
cvpred 1.00064 0.8957 0.8978 0.9664 0.9659 0.6521
LTR 0.99800 0.9310 0.9310 0.8880 0.9410 0.6060
CV residual -0.00264 0.0353 0.0332 -0.0784 -0.0249 -0.0461
Paraguay Poland Puerto Rico Qatar Saudi Arabia Slovenia
Predicted 0.8612 0.98637 0.9833 0.871 1.007 0.98938
cvpred 0.8433 0.99075 1.0035 0.825 1.002 0.99356
LTR 0.9390 0.99500 0.9040 0.963 0.866 0.99700
CV residual 0.0957 0.00425 -0.0995 0.138 -0.136 0.00344
Tajikistan Tanzania Trinidad and Tobago Turkmenistan Ukraine
Predicted 0.794 0.6756 0.9322 0.793 0.9184
cvpred 0.766 0.6497 0.9205 0.774 0.9132
LTR 0.997 0.7320 0.9880 0.996 0.9970
CV residual 0.231 0.0823 0.0675 0.222 0.0838
Vanuatu
Predicted 0.8060
cvpred 0.7799
LTR 0.8260
CV residual 0.0461
Sum of squares = 0.2 Mean square = 0.01 n = 31
fold 2
Observations in test set: 32
Angola Canada Chad China Congo, Dem. Rep. Dominican Republic
Predicted 0.7081 0.9666 0.594 0.835 0.606 0.8948
cvpred 0.6854 0.9561 0.570 0.820 0.511 0.8831
LTR 0.7010 0.9900 0.345 0.943 0.668 0.8950
CV residual 0.0156 0.0339 -0.225 0.123 0.157 0.0119
Egypt, Arab Rep. France Honduras Hungary Iraq Italy
Predicted 0.865 0.9882 0.8821 0.9714 0.8532 1.048
cvpred 0.859 0.9795 0.8844 0.9762 0.8372 1.056
LTR 0.720 0.9900 0.8480 0.9900 0.7820 0.989
CV residual -0.139 0.0105 -0.0364 0.0138 -0.0552 -0.067
Jamaica Japan Kazakhstan Kenya Mozambique Portugal Romania
Predicted 0.9469 0.99898 0.9134 0.792 0.6020 0.9946 0.9492
cvpred 0.9478 0.99767 0.9317 0.737 0.5777 0.9922 0.9587
LTR 0.8660 0.99000 0.9970 0.874 0.5610 0.9520 0.9770
CV residual -0.0818 -0.00767 0.0653 0.137 -0.0167 -0.0402 0.0183
Russian Federation Samoa South Africa Sudan Suriname Sweden
Predicted 0.96452 0.803 0.8518 0.72881 0.9584 1.0213
cvpred 0.99102 0.743 0.8553 0.70432 0.9787 1.0228
LTR 0.99600 0.988 0.9300 0.71100 0.9470 0.9900
CV residual 0.00498 0.245 0.0747 0.00668 -0.0317 -0.0328
Syrian Arab Republic Uganda United Arab Emirates
Predicted 0.8277 0.612 0.9129
cvpred 0.8015 0.592 0.9021
LTR 0.8340 0.732 0.9000
CV residual 0.0325 0.140 -0.0021
United Kingdom Uruguay Uzbekistan Zambia
Predicted 1.0207 0.98017 0.790 0.6737
cvpred 1.0267 0.98973 0.792 0.6528
LTR 0.9900 0.98100 0.994 0.7120
CV residual -0.0367 -0.00873 0.202 0.0592
Sum of squares = 0.29 Mean square = 0.01 n = 32
fold 3
Observations in test set: 32
Antigua and Barbuda Argentina Bangladesh
Predicted 1.0237 0.9528 0.739
cvpred 1.0123 0.9502 0.796
LTR 0.9900 0.9780 0.568
CV residual -0.0223 0.0278 -0.228
Bosnia and Herzegovina Botswana Costa Rica Croatia Cyprus
Predicted 0.9535 0.8096 0.892 0.9826 0.964
cvpred 0.9671 0.7518 0.920 0.9767 0.962
LTR 0.9790 0.8450 0.962 0.9880 0.983
CV residual 0.0119 0.0932 0.042 0.0113 0.021
Ecuador Equatorial Guinea Finland Gabon Georgia Guatemala
Predicted 0.89867 0.772 1.0460 0.8721 0.9128 0.873
cvpred 0.92582 0.722 1.0265 0.8523 0.9345 0.900
LTR 0.91900 0.939 0.9990 0.8840 0.9970 0.752
CV residual -0.00682 0.217 -0.0275 0.0317 0.0625 -0.148
Lithuania Macedonia, FYR Mali Moldova Mongolia Montenegro
Predicted 1.02530 0.9934 0.647 0.844 0.817 1.0265
cvpred 1.00228 0.9964 0.676 0.868 0.840 1.0212
LTR 0.99700 0.9730 0.311 0.985 0.974 0.9840
CV residual -0.00528 -0.0234 -0.365 0.117 0.134 -0.0372
Nepal Netherlands Nigeria Serbia Singapore Spain Sri Lanka
Predicted 0.675 1.00377 0.705 0.97553 1.0185 1.0417 0.87434
cvpred 0.735 0.99231 0.704 0.97779 1.0119 1.0321 0.90261
LTR 0.603 0.99000 0.613 0.97900 0.9590 0.9770 0.91200
CV residual -0.132 -0.00231 -0.091 0.00121 -0.0529 -0.0551 0.00939
Switzerland Timor-Leste United States Vietnam Yemen, Rep.
Predicted 1.0296 0.695 0.9799 0.88445 0.726
cvpred 1.0133 0.749 0.9645 0.93455 0.757
LTR 0.9900 0.583 0.9900 0.93200 0.639
CV residual -0.0233 -0.166 0.0255 -0.00255 -0.118
Sum of squares = 0.38 Mean square = 0.01 n = 32
Overall (Sum over all 32 folds)
ms
0.00917
CVlm(df=ltrdata10, form.lm=g)
Analysis of Variance Table
Response: LTR
Df Sum Sq Mean Sq F value Pr(>F)
GDP 1 0.932 0.932 118.89 < 2e-16
UNEMP 1 0.006 0.006 0.71 0.4002
URBGR 1 0.158 0.158 20.19 2.1e-05
MOBILE 1 0.176 0.176 22.45 8.2e-06
INTERNET 1 0.003 0.003 0.34 0.5624
LEXP 1 0.077 0.077 9.79 0.0024
Residuals 88 0.689 0.008
Warning:
As there is >1 explanatory variable, cross-validation predicted values for
a fold are not a linear function of corresponding overall predicted
values. Lines that are shown for the different folds are approximate
fold 1
Observations in test set: 31
Armenia Aruba Bahrain Brazil Brunei Darussalam Colombia
Predicted 0.978247 0.9794 0.9193 0.9411 0.96290 0.9148
cvpred 0.996596 0.9786 0.8971 0.9415 0.95937 0.9151
LTR 0.996000 0.9680 0.9190 0.9040 0.95200 0.9340
CV residual -0.000596 -0.0106 0.0219 -0.0375 -0.00737 0.0189
El Salvador Estonia Germany Ghana Greece India Jordan
Predicted 0.9197 0.99018 1.02 0.7515 1.0202 0.7702 0.9158
cvpred 0.9166 0.99368 1.02 0.7292 1.0436 0.7513 0.9159
LTR 0.8450 0.99800 0.99 0.6730 0.9720 0.7400 0.9260
CV residual -0.0716 0.00432 -0.03 -0.0562 -0.0716 -0.0113 0.0101
Latvia Malaysia Mexico Namibia Panama Papua New Guinea
Predicted 0.971 0.9074 0.9131 0.935 0.9843 0.6729
cvpred 0.980 0.8822 0.9147 0.998 0.9719 0.6602
LTR 0.998 0.9310 0.9310 0.888 0.9410 0.6060
CV residual 0.018 0.0488 0.0163 -0.110 -0.0309 -0.0542
Paraguay Poland Puerto Rico Qatar Saudi Arabia Slovenia
Predicted 0.8658 0.9801 0.992 0.867 1.013 0.9844
cvpred 0.8542 0.9786 1.024 0.816 1.016 0.9839
LTR 0.9390 0.9950 0.904 0.963 0.866 0.9970
CV residual 0.0848 0.0164 -0.120 0.147 -0.150 0.0131
Tajikistan Tanzania Trinidad and Tobago Turkmenistan Ukraine
Predicted 0.791 0.6679 0.9308 0.804 0.9201
cvpred 0.761 0.6349 0.9177 0.798 0.9178
LTR 0.997 0.7320 0.9880 0.996 0.9970
CV residual 0.236 0.0971 0.0703 0.198 0.0792
Vanuatu
Predicted 0.8154
cvpred 0.8004
LTR 0.8260
CV residual 0.0256
Sum of squares = 0.22 Mean square = 0.01 n = 31
fold 2
Observations in test set: 32
Angola Canada Chad China Congo, Dem. Rep. Dominican Republic
Predicted 0.7110 0.9616 0.588 0.836 0.598 0.89786
cvpred 0.6816 0.9464 0.551 0.820 0.485 0.88741
LTR 0.7010 0.9900 0.345 0.943 0.668 0.89500
CV residual 0.0194 0.0436 -0.206 0.123 0.183 0.00759
Egypt, Arab Rep. France Honduras Hungary Iraq Italy
Predicted 0.862 0.9827 0.8890 0.963 0.8682 1.0550
cvpred 0.855 0.9699 0.8975 0.963 0.8603 1.0703
LTR 0.720 0.9900 0.8480 0.990 0.7820 0.9890
CV residual -0.135 0.0201 -0.0495 0.027 -0.0783 -0.0813
Jamaica Japan Kazakhstan Kenya Mozambique Portugal Romania
Predicted 0.9513 0.99525 0.9165 0.789 0.59095 0.9981 0.9497
cvpred 0.9564 0.99183 0.9369 0.727 0.55185 0.9987 0.9607
LTR 0.8660 0.99000 0.9970 0.874 0.56100 0.9520 0.9770
CV residual -0.0904 -0.00183 0.0601 0.147 0.00915 -0.0467 0.0163
Russian Federation Samoa South Africa Sudan Suriname Sweden
Predicted 0.96324 0.816 0.8526 0.7256 0.9624 1.0121
cvpred 0.99011 0.759 0.8521 0.6941 0.9869 1.0079
LTR 0.99600 0.988 0.9300 0.7110 0.9470 0.9900
CV residual 0.00589 0.229 0.0779 0.0169 -0.0399 -0.0179
Syrian Arab Republic Uganda United Arab Emirates
Predicted 0.8329 0.602 0.9115
cvpred 0.8088 0.568 0.8974
LTR 0.8340 0.732 0.9000
CV residual 0.0252 0.164 0.0026
United Kingdom Uruguay Uzbekistan Zambia
Predicted 1.0115 0.9816 0.787 0.6697
cvpred 1.0124 0.9938 0.786 0.6395
LTR 0.9900 0.9810 0.994 0.7120
CV residual -0.0224 -0.0128 0.208 0.0725
Sum of squares = 0.3 Mean square = 0.01 n = 32
fold 3
Observations in test set: 32
Antigua and Barbuda Argentina Bangladesh
Predicted 1.0085 0.9519 0.741
cvpred 1.0219 0.9511 0.796
LTR 0.9900 0.9780 0.568
CV residual -0.0319 0.0269 -0.228
Bosnia and Herzegovina Botswana Costa Rica Croatia Cyprus
Predicted 0.94822 0.8144 0.8976 0.9802 0.9692
cvpred 0.97231 0.7459 0.9177 0.9788 0.9593
LTR 0.97900 0.8450 0.9620 0.9880 0.9830
CV residual 0.00669 0.0991 0.0443 0.0092 0.0237
Ecuador Equatorial Guinea Finland Gabon Georgia Guatemala
Predicted 0.90272 0.786 1.0368 0.886 0.915 0.882
cvpred 0.92437 0.711 1.0322 0.843 0.935 0.896
LTR 0.91900 0.939 0.9990 0.884 0.997 0.752
CV residual -0.00537 0.228 -0.0332 0.041 0.062 -0.144
Lithuania Macedonia, FYR Mali Moldova Mongolia Montenegro
Predicted 1.0178 0.9883 0.642 0.837 0.822 1.030
cvpred 1.0076 1.0017 0.677 0.873 0.837 1.021
LTR 0.9970 0.9730 0.311 0.985 0.974 0.984
CV residual -0.0106 -0.0287 -0.366 0.112 0.137 -0.037
Nepal Netherlands Nigeria Serbia Singapore Spain
Predicted 0.673 0.99296 0.6938 0.974830 1.0177 1.0433
cvpred 0.737 0.99861 0.7089 0.979719 1.0126 1.0325
LTR 0.603 0.99000 0.6130 0.979000 0.9590 0.9770
CV residual -0.134 -0.00861 -0.0959 -0.000719 -0.0536 -0.0555
Sri Lanka Switzerland Timor-Leste United States Vietnam
Predicted 0.8820 1.0256 0.697 0.977 0.8795
cvpred 0.8992 1.0156 0.748 0.966 0.9393
LTR 0.9120 0.9900 0.583 0.990 0.9320
CV residual 0.0128 -0.0256 -0.165 0.024 -0.0073
Yemen, Rep.
Predicted 0.726
cvpred 0.757
LTR 0.639
CV residual -0.118
Sum of squares = 0.39 Mean square = 0.01 n = 32
Overall (Sum over all 32 folds)
ms
0.00956
# Use a different seed for choosing different random folds
(seed <- round(runif(1, min=0, max=100)))
[1] 16
CVlm(df=ltrdata10, form.lm=g.step, seed=seed)
Analysis of Variance Table
Response: LTR
Df Sum Sq Mean Sq F value Pr(>F)
GDP 1 0.932 0.932 119.54 < 2e-16
UNEMP 1 0.006 0.006 0.72 0.3989
URBGR 1 0.158 0.158 20.30 2.0e-05
MOBILE 1 0.176 0.176 22.57 7.7e-06
LEXP 1 0.075 0.075 9.66 0.0025
Residuals 89 0.694 0.008
Warning:
As there is >1 explanatory variable, cross-validation predicted values for
a fold are not a linear function of corresponding overall predicted
values. Lines that are shown for the different folds are approximate
fold 1
Observations in test set: 31
Argentina Brazil Croatia Dominican Republic France Germany
Predicted 0.9528 0.9375 0.9826 0.89483 0.98818 1.0281
cvpred 0.9479 0.9328 0.9913 0.88747 0.98527 1.0331
LTR 0.9780 0.9040 0.9880 0.89500 0.99000 0.9900
CV residual 0.0301 -0.0288 -0.0033 0.00753 0.00473 -0.0431
Greece Hungary Iraq Jamaica Jordan Macedonia, FYR Malaysia
Predicted 1.0101 0.9714 0.8532 0.9469 0.9113 0.9934 0.9140
cvpred 1.0156 0.9767 0.8513 0.9544 0.8991 1.0209 0.8884
LTR 0.9720 0.9900 0.7820 0.8660 0.9260 0.9730 0.9310
CV residual -0.0436 0.0133 -0.0693 -0.0884 0.0269 -0.0479 0.0426
Mali Mongolia Montenegro Nigeria Panama Papua New Guinea
Predicted 0.647 0.817 1.0265 0.7050 0.9819 0.669
cvpred 0.628 0.796 1.0335 0.7085 0.9531 0.674
LTR 0.311 0.974 0.9840 0.6130 0.9410 0.606
CV residual -0.317 0.178 -0.0495 -0.0955 -0.0121 -0.068
Poland Portugal Qatar Romania Sweden Tajikistan
Predicted 0.98637 0.9946 0.871 0.9492 1.0213 0.794
cvpred 0.99342 0.9938 0.772 0.9564 1.0186 0.775
LTR 0.99500 0.9520 0.963 0.9770 0.9900 0.997
CV residual 0.00158 -0.0418 0.191 0.0206 -0.0286 0.222
Trinidad and Tobago Turkmenistan Uganda United Arab Emirates
Predicted 0.9322 0.793 0.612 0.9129
cvpred 0.9176 0.788 0.580 0.8378
LTR 0.9880 0.996 0.732 0.9000
CV residual 0.0704 0.208 0.152 0.0622
Vanuatu Vietnam
Predicted 0.8060 0.8844
cvpred 0.7794 0.8514
LTR 0.8260 0.9320
CV residual 0.0466 0.0806
Sum of squares = 0.34 Mean square = 0.01 n = 31
fold 2
Observations in test set: 32
Armenia Aruba Bangladesh Brunei Darussalam China Colombia
Predicted 0.9737 0.9823 0.739 0.95844 0.835 0.9131
cvpred 0.9776 0.9805 0.726 0.95538 0.825 0.9132
LTR 0.9960 0.9680 0.568 0.95200 0.943 0.9340
CV residual 0.0184 -0.0125 -0.158 -0.00338 0.118 0.0208
Costa Rica Ecuador Egypt, Arab Rep. El Salvador Finland
Predicted 0.8920 0.8987 0.865 0.9125 1.0460
cvpred 0.8692 0.9062 0.868 0.9295 1.0476
LTR 0.9620 0.9190 0.720 0.8450 0.9990
CV residual 0.0928 0.0128 -0.148 -0.0845 -0.0486
Gabon Georgia Ghana Guatemala Honduras India Japan
Predicted 0.87207 0.9128 0.7515 0.873 0.8821 0.7678 0.9990
cvpred 0.89124 0.9096 0.7696 0.902 0.9085 0.7686 0.9776
LTR 0.88400 0.9970 0.6730 0.752 0.8480 0.7400 0.9900
CV residual -0.00724 0.0874 -0.0966 -0.150 -0.0605 -0.0286 0.0124
Kazakhstan Mexico Moldova Mozambique Russian Federation Samoa
Predicted 0.9134 0.9056 0.844 0.6020 0.96452 0.803
cvpred 0.9272 0.8933 0.853 0.5955 0.98862 0.729
LTR 0.9970 0.9310 0.985 0.5610 0.99600 0.988
CV residual 0.0698 0.0377 0.132 -0.0345 0.00738 0.259
Saudi Arabia Singapore Slovenia United Kingdom United States
Predicted 1.007 1.0185 0.9894 1.0207 0.98
cvpred 1.033 1.0217 0.9747 1.0157 0.96
LTR 0.866 0.9590 0.9970 0.9900 0.99
CV residual -0.167 -0.0627 0.0223 -0.0257 0.03
Uruguay Uzbekistan Yemen, Rep.
Predicted 0.98017 0.790 0.7265
cvpred 0.98436 0.801 0.7213
LTR 0.98100 0.994 0.6390
CV residual -0.00336 0.193 -0.0823
Sum of squares = 0.29 Mean square = 0.01 n = 32
fold 3
Observations in test set: 32
Angola Antigua and Barbuda Bahrain Bosnia and Herzegovina
Predicted 0.7081 1.02366 0.91953 0.9535
cvpred 0.6092 0.99941 0.92231 0.9233
LTR 0.7010 0.99000 0.91900 0.9790
CV residual 0.0918 -0.00941 -0.00331 0.0557
Botswana Canada Chad Congo, Dem. Rep. Cyprus
Predicted 0.810 0.966587 0.594 0.606 0.96431
cvpred 0.685 0.990849 0.569 0.489 0.98501
LTR 0.845 0.990000 0.345 0.668 0.98300
CV residual 0.160 -0.000849 -0.224 0.179 -0.00201
Equatorial Guinea Estonia Italy Kenya Latvia Lithuania
Predicted 0.772 1.0012 1.0478 0.792 0.9812 1.02530
cvpred 0.676 0.9761 1.0519 0.686 0.9555 0.98945
LTR 0.939 0.9980 0.9890 0.874 0.9980 0.99700
CV residual 0.263 0.0219 -0.0629 0.188 0.0425 0.00755
Namibia Nepal Netherlands Paraguay Puerto Rico Serbia
Predicted 0.923 0.675 1.0038 0.8612 0.9833 0.976
cvpred 0.768 0.735 1.0226 0.8759 0.9821 0.948
LTR 0.888 0.603 0.9900 0.9390 0.9040 0.979
CV residual 0.120 -0.132 -0.0326 0.0631 -0.0781 0.031
South Africa Spain Sri Lanka Sudan Suriname Switzerland
Predicted 0.852 1.0417 0.8743 0.7288 0.9584 1.0296
cvpred 0.740 1.0247 0.9074 0.7201 0.9316 1.0469
LTR 0.930 0.9770 0.9120 0.7110 0.9470 0.9900
CV residual 0.190 -0.0477 0.0046 -0.0091 0.0154 -0.0569
Syrian Arab Republic Tanzania Timor-Leste Ukraine Zambia
Predicted 0.8277 0.6756 0.695 0.9184 0.6737
cvpred 0.8617 0.6677 0.732 0.9173 0.6347
LTR 0.8340 0.7320 0.583 0.9970 0.7120
CV residual -0.0277 0.0643 -0.149 0.0797 0.0773
Sum of squares = 0.36 Mean square = 0.01 n = 32
Overall (Sum over all 32 folds)
ms
0.0105
CVlm(df=ltrdata10, form.lm=g, seed=seed)
Analysis of Variance Table
Response: LTR
Df Sum Sq Mean Sq F value Pr(>F)
GDP 1 0.932 0.932 118.89 < 2e-16
UNEMP 1 0.006 0.006 0.71 0.4002
URBGR 1 0.158 0.158 20.19 2.1e-05
MOBILE 1 0.176 0.176 22.45 8.2e-06
INTERNET 1 0.003 0.003 0.34 0.5624
LEXP 1 0.077 0.077 9.79 0.0024
Residuals 88 0.689 0.008
Warning:
As there is >1 explanatory variable, cross-validation predicted values for
a fold are not a linear function of corresponding overall predicted
values. Lines that are shown for the different folds are approximate
fold 1
Observations in test set: 31
Argentina Brazil Croatia Dominican Republic France Germany
Predicted 0.9519 0.9411 0.98020 0.89786 0.9827 1.0207
cvpred 0.9467 0.9377 0.98915 0.89057 0.9771 1.0239
LTR 0.9780 0.9040 0.98800 0.89500 0.9900 0.9900
CV residual 0.0313 -0.0337 -0.00115 0.00443 0.0129 -0.0339
Greece Hungary Iraq Jamaica Jordan Macedonia, FYR Malaysia
Predicted 1.0202 0.9632 0.8682 0.9513 0.9158 0.9883 0.9074
cvpred 1.0292 0.9663 0.8706 0.9618 0.9038 1.0148 0.8774
LTR 0.9720 0.9900 0.7820 0.8660 0.9260 0.9730 0.9310
CV residual -0.0572 0.0237 -0.0886 -0.0958 0.0222 -0.0418 0.0536
Mali Mongolia Montenegro Nigeria Panama Papua New Guinea
Predicted 0.642 0.822 1.0296 0.6938 0.9843 0.6729
cvpred 0.620 0.802 1.0377 0.6918 0.9535 0.6809
LTR 0.311 0.974 0.9840 0.6130 0.9410 0.6060
CV residual -0.309 0.172 -0.0537 -0.0788 -0.0125 -0.0749
Poland Portugal Qatar Romania Sweden Tajikistan
Predicted 0.98010 0.9981 0.867 0.9497 1.0121 0.791
cvpred 0.98638 0.9981 0.752 0.9592 1.0055 0.772
LTR 0.99500 0.9520 0.963 0.9770 0.9900 0.997
CV residual 0.00862 -0.0461 0.211 0.0178 -0.0155 0.225
Trinidad and Tobago Turkmenistan Uganda United Arab Emirates
Predicted 0.9308 0.804 0.602 0.9115
cvpred 0.9139 0.804 0.564 0.8241
LTR 0.9880 0.996 0.732 0.9000
CV residual 0.0741 0.192 0.168 0.0759
Vanuatu Vietnam
Predicted 0.8154 0.8795
cvpred 0.7904 0.8431
LTR 0.8260 0.9320
CV residual 0.0356 0.0889
Sum of squares = 0.35 Mean square = 0.01 n = 31
fold 2
Observations in test set: 32
Armenia Aruba Bangladesh Brunei Darussalam China Colombia
Predicted 0.9782 0.97944 0.741 0.96290 0.836 0.9148
cvpred 0.9847 0.97683 0.731 0.96073 0.827 0.9162
LTR 0.9960 0.96800 0.568 0.95200 0.943 0.9340
CV residual 0.0113 -0.00883 -0.163 -0.00873 0.116 0.0178
Costa Rica Ecuador Egypt, Arab Rep. El Salvador Finland
Predicted 0.8976 0.90272 0.862 0.9197 1.0368
cvpred 0.8772 0.91246 0.867 0.9391 1.0367
LTR 0.9620 0.91900 0.720 0.8450 0.9990
CV residual 0.0848 0.00654 -0.147 -0.0941 -0.0377
Gabon Georgia Ghana Guatemala Honduras India Japan
Predicted 0.8862 0.9148 0.7515 0.882 0.8890 0.7702 0.9952
cvpred 0.9077 0.9137 0.7705 0.913 0.9185 0.7725 0.9734
LTR 0.8840 0.9970 0.6730 0.752 0.8480 0.7400 0.9900
CV residual -0.0237 0.0833 -0.0975 -0.161 -0.0705 -0.0325 0.0166
Kazakhstan Mexico Moldova Mozambique Russian Federation Samoa
Predicted 0.9165 0.9131 0.837 0.5909 0.96324 0.816
cvpred 0.9308 0.9031 0.846 0.5828 0.98697 0.745
LTR 0.9970 0.9310 0.985 0.5610 0.99600 0.988
CV residual 0.0662 0.0279 0.139 -0.0218 0.00903 0.243
Saudi Arabia Singapore Slovenia United Kingdom United States
Predicted 1.013 1.0177 0.9844 1.0115 0.9771
cvpred 1.041 1.0209 0.9691 1.0051 0.9566
LTR 0.866 0.9590 0.9970 0.9900 0.9900
CV residual -0.175 -0.0619 0.0279 -0.0151 0.0334
Uruguay Uzbekistan Yemen, Rep.
Predicted 0.98160 0.787 0.7263
cvpred 0.98667 0.798 0.7222
LTR 0.98100 0.994 0.6390
CV residual -0.00567 0.196 -0.0832
Sum of squares = 0.29 Mean square = 0.01 n = 32
fold 3
Observations in test set: 32
Angola Antigua and Barbuda Bahrain Bosnia and Herzegovina
Predicted 0.7110 1.00851 0.91934 0.9482
cvpred 0.6112 0.99496 0.92245 0.9209
LTR 0.7010 0.99000 0.91900 0.9790
CV residual 0.0898 -0.00496 -0.00345 0.0581
Botswana Canada Chad Congo, Dem. Rep. Cyprus
Predicted 0.814 0.961566 0.588 0.598 0.9692
cvpred 0.688 0.989304 0.568 0.486 0.9864
LTR 0.845 0.990000 0.345 0.668 0.9830
CV residual 0.157 0.000696 -0.223 0.182 -0.0034
Equatorial Guinea Estonia Italy Kenya Latvia Lithuania
Predicted 0.786 0.9902 1.055 0.789 0.9706 1.01779
cvpred 0.682 0.9728 1.054 0.685 0.9522 0.98718
LTR 0.939 0.9980 0.989 0.874 0.9980 0.99700
CV residual 0.257 0.0252 -0.065 0.189 0.0458 0.00982
Namibia Nepal Netherlands Paraguay Puerto Rico Serbia
Predicted 0.935 0.673 0.9930 0.866 0.9922 0.9748
cvpred 0.772 0.734 1.0195 0.877 0.9846 0.9473
LTR 0.888 0.603 0.9900 0.939 0.9040 0.9790
CV residual 0.116 -0.131 -0.0295 0.062 -0.0806 0.0317
South Africa Spain Sri Lanka Sudan Suriname Switzerland
Predicted 0.853 1.0433 0.88202 0.72559 0.9624 1.0256
cvpred 0.741 1.0248 0.90906 0.71902 0.9331 1.0458
LTR 0.930 0.9770 0.91200 0.71100 0.9470 0.9900
CV residual 0.189 -0.0478 0.00294 -0.00802 0.0139 -0.0558
Syrian Arab Republic Tanzania Timor-Leste Ukraine Zambia
Predicted 0.8329 0.6679 0.697 0.9201 0.6697
cvpred 0.8625 0.6651 0.733 0.9176 0.6339
LTR 0.8340 0.7320 0.583 0.9970 0.7120
CV residual -0.0285 0.0669 -0.150 0.0794 0.0781
Sum of squares = 0.35 Mean square = 0.01 n = 32
Overall (Sum over all 32 folds)
ms
0.0105
# Small dataset here, m = 4 folds
seed <- round(runif(1, min=0, max=100))
CVlm(df=ltrdata10, form.lm=g.step, m=4)
Analysis of Variance Table
Response: LTR
Df Sum Sq Mean Sq F value Pr(>F)
GDP 1 0.932 0.932 119.54 < 2e-16
UNEMP 1 0.006 0.006 0.72 0.3989
URBGR 1 0.158 0.158 20.30 2.0e-05
MOBILE 1 0.176 0.176 22.57 7.7e-06
LEXP 1 0.075 0.075 9.66 0.0025
Residuals 89 0.694 0.008
Warning:
As there is >1 explanatory variable, cross-validation predicted values for
a fold are not a linear function of corresponding overall predicted
values. Lines that are shown for the different folds are approximate
fold 1
Observations in test set: 23
Brunei Darussalam China Cyprus Dominican Republic El Salvador
Predicted 0.95844 0.835 0.9643 0.89483 0.9125
cvpred 0.94636 0.822 0.9565 0.89142 0.9182
LTR 0.95200 0.943 0.9830 0.89500 0.8450
CV residual 0.00564 0.121 0.0265 0.00358 -0.0732
Ghana Japan Latvia Lithuania Macedonia, FYR Malaysia
Predicted 0.751 0.998979 0.981234 1.0253 0.9934 0.9140
cvpred 0.748 0.990961 0.998192 1.0488 1.0088 0.9028
LTR 0.673 0.990000 0.998000 0.9970 0.9730 0.9310
CV residual -0.075 -0.000961 -0.000192 -0.0518 -0.0358 0.0282
Moldova Montenegro Mozambique Nepal Netherlands Paraguay
Predicted 0.844 1.0265 0.6020 0.6750 1.00377 0.8612
cvpred 0.852 1.0394 0.6109 0.6708 0.99616 0.8562
LTR 0.985 0.9840 0.5610 0.6030 0.99000 0.9390
CV residual 0.133 -0.0554 -0.0499 -0.0678 -0.00616 0.0828
Qatar Romania Singapore Suriname Sweden Zambia
Predicted 0.871 0.9492 1.0185 0.9584 1.0213 0.6737
cvpred 0.791 0.9618 1.0067 0.9628 1.0145 0.6705
LTR 0.963 0.9770 0.9590 0.9470 0.9900 0.7120
CV residual 0.172 0.0152 -0.0477 -0.0158 -0.0245 0.0415
Sum of squares = 0.1 Mean square = 0 n = 23
fold 2
Observations in test set: 24
Bahrain Bosnia and Herzegovina Brazil Chad Costa Rica
Predicted 0.91953 0.9535 0.9375 0.594 0.8920
cvpred 0.92217 0.9286 0.9314 0.604 0.8701
LTR 0.91900 0.9790 0.9040 0.345 0.9620
CV residual -0.00317 0.0504 -0.0274 -0.259 0.0919
Croatia Estonia France Georgia Guatemala Honduras Jordan
Predicted 0.9826 1.00116 0.9882 0.913 0.873 0.8821 0.9113
cvpred 0.9745 0.99465 0.9759 0.896 0.874 0.8759 0.9028
LTR 0.9880 0.99800 0.9900 0.997 0.752 0.8480 0.9260
CV residual 0.0135 0.00335 0.0141 0.101 -0.122 -0.0279 0.0232
Kazakhstan Nigeria Poland Puerto Rico Samoa Switzerland
Predicted 0.9134 0.705 0.9864 0.9833 0.803 1.0296
cvpred 0.9247 0.724 0.9804 0.9688 0.766 1.0258
LTR 0.9970 0.613 0.9950 0.9040 0.988 0.9900
CV residual 0.0723 -0.111 0.0146 -0.0648 0.222 -0.0358
Syrian Arab Republic Tanzania Timor-Leste Uganda Uzbekistan
Predicted 0.8277 0.6756 0.6945 0.612 0.790
cvpred 0.8067 0.6742 0.6827 0.616 0.787
LTR 0.8340 0.7320 0.5830 0.732 0.994
CV residual 0.0273 0.0578 -0.0997 0.116 0.207
Vanuatu
Predicted 0.8060
cvpred 0.8005
LTR 0.8260
CV residual 0.0255
Sum of squares = 0.25 Mean square = 0.01 n = 24
fold 3
Observations in test set: 24
Angola Armenia Aruba Bangladesh Canada Ecuador
Predicted 0.70808 0.9737 0.98234 0.739 0.9666 0.899
cvpred 0.69377 0.9801 0.97653 0.759 0.9722 0.908
LTR 0.70100 0.9960 0.96800 0.568 0.9900 0.919
CV residual 0.00723 0.0159 -0.00853 -0.191 0.0178 0.011
Egypt, Arab Rep. Gabon Greece India Jamaica Mexico
Predicted 0.865 0.8721 1.0101 0.7678 0.9469 0.906
cvpred 0.870 0.8585 1.0145 0.7739 0.9487 0.914
LTR 0.720 0.8840 0.9720 0.7400 0.8660 0.931
CV residual -0.150 0.0255 -0.0425 -0.0339 -0.0827 0.017
Mongolia Portugal Russian Federation Saudi Arabia Serbia
Predicted 0.817 0.9946 0.9645 1.007 0.975530
cvpred 0.819 0.9977 0.9514 1.001 0.979304
LTR 0.974 0.9520 0.9960 0.866 0.979000
CV residual 0.155 -0.0457 0.0446 -0.135 -0.000304
South Africa Sri Lanka Trinidad and Tobago Ukraine
Predicted 0.852 0.8743 0.9322 0.9184
cvpred 0.829 0.8849 0.9215 0.9182
LTR 0.930 0.9120 0.9880 0.9970
CV residual 0.101 0.0271 0.0665 0.0788
United States Uruguay Yemen, Rep.
Predicted 0.97991 0.980174 0.7265
cvpred 0.98001 0.980739 0.7346
LTR 0.99000 0.981000 0.6390
CV residual 0.00999 0.000261 -0.0956
Sum of squares = 0.15 Mean square = 0.01 n = 24
fold 4
Observations in test set: 24
Antigua and Barbuda Argentina Botswana Colombia
Predicted 1.0237 0.9528 0.8096 0.9131
cvpred 1.0232 0.9508 0.7719 0.9154
LTR 0.9900 0.9780 0.8450 0.9340
CV residual -0.0332 0.0272 0.0731 0.0186
Congo, Dem. Rep. Equatorial Guinea Finland Germany Hungary
Predicted 0.6061 0.772 1.0460 1.0281 0.9714
cvpred 0.5943 0.742 1.0479 1.0275 0.9683
LTR 0.6680 0.939 0.9990 0.9900 0.9900
CV residual 0.0737 0.197 -0.0489 -0.0375 0.0217
Iraq Italy Kenya Mali Namibia Panama Papua New Guinea
Predicted 0.8532 1.0478 0.7916 0.647 0.9229 0.9819 0.6694
cvpred 0.8521 1.0538 0.7919 0.636 0.9196 0.9929 0.6571
LTR 0.7820 0.9890 0.8740 0.311 0.8880 0.9410 0.6060
CV residual -0.0701 -0.0648 0.0821 -0.325 -0.0316 -0.0519 -0.0511
Slovenia Spain Sudan Tajikistan Turkmenistan
Predicted 0.98938 1.0417 0.72881 0.794 0.793
cvpred 0.99054 1.0486 0.71907 0.794 0.781
LTR 0.99700 0.9770 0.71100 0.997 0.996
CV residual 0.00646 -0.0716 -0.00807 0.203 0.215
United Arab Emirates United Kingdom Vietnam
Predicted 0.9129 1.0207 0.8844
cvpred 0.9413 1.0247 0.8989
LTR 0.9000 0.9900 0.9320
CV residual -0.0413 -0.0347 0.0331
Sum of squares = 0.28 Mean square = 0.01 n = 24
Overall (Sum over all 24 folds)
ms
0.00819
CVlm(df=ltrdata10, form.lm=g, m=4)
Analysis of Variance Table
Response: LTR
Df Sum Sq Mean Sq F value Pr(>F)
GDP 1 0.932 0.932 118.89 < 2e-16
UNEMP 1 0.006 0.006 0.71 0.4002
URBGR 1 0.158 0.158 20.19 2.1e-05
MOBILE 1 0.176 0.176 22.45 8.2e-06
INTERNET 1 0.003 0.003 0.34 0.5624
LEXP 1 0.077 0.077 9.79 0.0024
Residuals 88 0.689 0.008
Warning:
As there is >1 explanatory variable, cross-validation predicted values for
a fold are not a linear function of corresponding overall predicted
values. Lines that are shown for the different folds are approximate
fold 1
Observations in test set: 23
Brunei Darussalam China Cyprus Dominican Republic El Salvador
Predicted 0.962904 0.836 0.9692 8.98e-01 0.9197
cvpred 0.951347 0.822 0.9618 8.95e-01 0.9284
LTR 0.952000 0.943 0.9830 8.95e-01 0.8450
CV residual 0.000653 0.121 0.0212 6.39e-05 -0.0834
Ghana Japan Latvia Lithuania Macedonia, FYR Malaysia
Predicted 0.7515 0.99525 0.9706 1.0178 0.9883 0.9074
cvpred 0.7477 0.98365 0.9813 1.0371 1.0004 0.8927
LTR 0.6730 0.99000 0.9980 0.9970 0.9730 0.9310
CV residual -0.0747 0.00635 0.0167 -0.0401 -0.0274 0.0383
Moldova Montenegro Mozambique Nepal Netherlands Paraguay
Predicted 0.837 1.0296 0.5909 0.6726 0.9930 0.8658
cvpred 0.841 1.0438 0.5936 0.6659 0.9789 0.8625
LTR 0.985 0.9840 0.5610 0.6030 0.9900 0.9390
CV residual 0.144 -0.0598 -0.0326 -0.0629 0.0111 0.0765
Qatar Romania Singapore Suriname Sweden Zambia
Predicted 0.867 0.9497 1.0177 0.9624 1.01213 0.6697
cvpred 0.785 0.9616 1.0044 0.9685 0.99949 0.6633
LTR 0.963 0.9770 0.9590 0.9470 0.99000 0.7120
CV residual 0.178 0.0154 -0.0454 -0.0215 -0.00949 0.0487
Sum of squares = 0.1 Mean square = 0 n = 23
fold 2
Observations in test set: 24
Bahrain Bosnia and Herzegovina Brazil Chad Costa Rica
Predicted 0.91934 0.9482 0.9411 0.588 0.8976
cvpred 0.92198 0.9262 0.9341 0.599 0.8751
LTR 0.91900 0.9790 0.9040 0.345 0.9620
CV residual -0.00298 0.0528 -0.0301 -0.254 0.0869
Croatia Estonia France Georgia Guatemala Honduras Jordan
Predicted 0.9802 0.9902 0.9827 0.9148 0.882 0.8890 0.916
cvpred 0.9734 0.9878 0.9733 0.8975 0.880 0.8804 0.906
LTR 0.9880 0.9980 0.9900 0.9970 0.752 0.8480 0.926
CV residual 0.0146 0.0102 0.0167 0.0995 -0.128 -0.0324 0.020
Kazakhstan Nigeria Poland Puerto Rico Samoa Switzerland
Predicted 0.9165 0.694 0.9801 0.9922 0.816 1.0256
cvpred 0.9261 0.716 0.9767 0.9755 0.776 1.0238
LTR 0.9970 0.613 0.9950 0.9040 0.988 0.9900
CV residual 0.0709 -0.103 0.0183 -0.0715 0.212 -0.0338
Syrian Arab Republic Tanzania Timor-Leste Uganda Uzbekistan
Predicted 0.8329 0.6679 0.697 0.602 0.787
cvpred 0.8111 0.6688 0.685 0.608 0.785
LTR 0.8340 0.7320 0.583 0.732 0.994
CV residual 0.0229 0.0632 -0.102 0.124 0.209
Vanuatu
Predicted 0.8154
cvpred 0.8068
LTR 0.8260
CV residual 0.0192
Sum of squares = 0.25 Mean square = 0.01 n = 24
fold 3
Observations in test set: 24
Angola Armenia Aruba Bangladesh Canada Ecuador
Predicted 0.71097 0.97825 0.979 0.741 0.9616 0.90272
cvpred 0.69812 0.98808 0.974 0.762 0.9655 0.91452
LTR 0.70100 0.99600 0.968 0.568 0.9900 0.91900
CV residual 0.00288 0.00792 -0.006 -0.194 0.0245 0.00448
Egypt, Arab Rep. Gabon Greece India Jamaica Mexico
Predicted 0.862 0.88616 1.0202 0.7702 0.9513 0.91314
cvpred 0.869 0.87829 1.0283 0.7784 0.9563 0.92451
LTR 0.720 0.88400 0.9720 0.7400 0.8660 0.93100
CV residual -0.149 0.00571 -0.0563 -0.0384 -0.0903 0.00649
Mongolia Portugal Russian Federation Saudi Arabia Serbia
Predicted 0.822 0.9981 0.963 1.013 0.97483
cvpred 0.826 1.0032 0.952 1.011 0.98023
LTR 0.974 0.9520 0.996 0.866 0.97900
CV residual 0.148 -0.0512 0.044 -0.145 -0.00123
South Africa Sri Lanka Trinidad and Tobago Ukraine
Predicted 0.8526 0.8820 0.9308 0.9201
cvpred 0.8318 0.8964 0.9213 0.9226
LTR 0.9300 0.9120 0.9880 0.9970
CV residual 0.0982 0.0156 0.0667 0.0744
United States Uruguay Yemen, Rep.
Predicted 0.9771 0.98160 0.726
cvpred 0.9767 0.98414 0.735
LTR 0.9900 0.98100 0.639
CV residual 0.0133 -0.00314 -0.096
Sum of squares = 0.15 Mean square = 0.01 n = 24
fold 4
Observations in test set: 24
Antigua and Barbuda Argentina Botswana Colombia
Predicted 1.0085 0.9519 0.8144 0.9148
cvpred 1.0247 0.9509 0.7709 0.9153
LTR 0.9900 0.9780 0.8450 0.9340
CV residual -0.0347 0.0271 0.0741 0.0187
Congo, Dem. Rep. Equatorial Guinea Finland Germany Hungary
Predicted 0.5975 0.786 1.0368 1.0207 0.963
cvpred 0.5948 0.740 1.0487 1.0282 0.969
LTR 0.6680 0.939 0.9990 0.9900 0.990
CV residual 0.0732 0.199 -0.0497 -0.0382 0.021
Iraq Italy Kenya Mali Namibia Panama Papua New Guinea
Predicted 0.8682 1.0550 0.7887 0.642 0.9354 0.9843 0.6729
cvpred 0.8507 1.0532 0.7921 0.636 0.9182 0.9929 0.6566
LTR 0.7820 0.9890 0.8740 0.311 0.8880 0.9410 0.6060
CV residual -0.0687 -0.0642 0.0819 -0.325 -0.0302 -0.0519 -0.0506
Slovenia Spain Sudan Tajikistan Turkmenistan
Predicted 0.98437 1.0433 0.72559 0.791 0.804
cvpred 0.99103 1.0485 0.71924 0.795 0.780
LTR 0.99700 0.9770 0.71100 0.997 0.996
CV residual 0.00597 -0.0715 -0.00824 0.202 0.216
United Arab Emirates United Kingdom Vietnam
Predicted 0.9115 1.0115 0.8795
cvpred 0.9414 1.0256 0.8998
LTR 0.9000 0.9900 0.9320
CV residual -0.0414 -0.0356 0.0322
Sum of squares = 0.28 Mean square = 0.01 n = 24
Overall (Sum over all 24 folds)
ms
0.00822
# Compare several cross-validation at one time
par(mfrow=c(2,3))
for(i in 1:3){
seed <- round(runif(1, min=0, max=100))
CVlm(df=ltrdata10, form.lm=g.step, m=4, seed=seed)
CVlm(df=ltrdata10, form.lm=g, m=4, seed=seed)}
Analysis of Variance Table
Response: LTR
Df Sum Sq Mean Sq F value Pr(>F)
GDP 1 0.932 0.932 119.54 < 2e-16
UNEMP 1 0.006 0.006 0.72 0.3989
URBGR 1 0.158 0.158 20.30 2.0e-05
MOBILE 1 0.176 0.176 22.57 7.7e-06
LEXP 1 0.075 0.075 9.66 0.0025
Residuals 89 0.694 0.008
Warning:
As there is >1 explanatory variable, cross-validation predicted values for
a fold are not a linear function of corresponding overall predicted
values. Lines that are shown for the different folds are approximate
fold 1
Observations in test set: 23
Brazil Brunei Darussalam Congo, Dem. Rep. Cyprus El Salvador
Predicted 0.9375 9.58e-01 0.606 0.9643 0.9125
cvpred 0.9399 9.52e-01 0.477 0.9498 0.9389
LTR 0.9040 9.52e-01 0.668 0.9830 0.8450
CV residual -0.0359 -3.43e-05 0.191 0.0332 -0.0939
Equatorial Guinea Georgia Germany Ghana Honduras Italy
Predicted 0.772 0.9128 1.0281 0.7515 0.8821 1.0478
cvpred 0.716 0.9126 1.0353 0.7439 0.9048 1.0583
LTR 0.939 0.9970 0.9900 0.6730 0.8480 0.9890
CV residual 0.223 0.0844 -0.0453 -0.0709 -0.0568 -0.0693
Jamaica Kenya Lithuania Montenegro Qatar Romania Samoa
Predicted 0.9469 0.792 1.025 1.027 0.871 0.94919 0.803
cvpred 0.9653 0.727 1.051 1.052 0.794 0.97253 0.728
LTR 0.8660 0.874 0.997 0.984 0.963 0.97700 0.988
CV residual -0.0993 0.147 -0.054 -0.068 0.169 0.00447 0.260
Slovenia Sri Lanka United Arab Emirates Uzbekistan Zambia
Predicted 0.98938 0.8743 0.913 0.790 0.6737
cvpred 0.99035 0.8897 0.854 0.805 0.6283
LTR 0.99700 0.9120 0.900 0.994 0.7120
CV residual 0.00665 0.0223 0.046 0.189 0.0837
Sum of squares = 0.3 Mean square = 0.01 n = 23
fold 2
Observations in test set: 24
Angola Bahrain Botswana Ecuador Egypt, Arab Rep. Estonia
Predicted 0.70808 0.91953 0.8096 0.8987 0.865 1.00116
cvpred 0.70842 0.92541 0.7866 0.9003 0.863 1.00398
LTR 0.70100 0.91900 0.8450 0.9190 0.720 0.99800
CV residual -0.00742 -0.00641 0.0584 0.0187 -0.143 -0.00598
Hungary India Moldova Mongolia Mozambique Nigeria Poland
Predicted 0.9714 0.768 0.844 0.817 0.602 0.7050 0.9864
cvpred 0.9695 0.760 0.838 0.809 0.592 0.7004 0.9838
LTR 0.9900 0.740 0.985 0.974 0.561 0.6130 0.9950
CV residual 0.0205 -0.020 0.147 0.165 -0.031 -0.0874 0.0112
Portugal Saudi Arabia Serbia Sweden Switzerland Tanzania
Predicted 0.9946 1.007 0.975530 1.0213 1.030 0.6756
cvpred 0.9992 1.006 0.979169 1.0263 1.032 0.6741
LTR 0.9520 0.866 0.979000 0.9900 0.990 0.7320
CV residual -0.0472 -0.140 -0.000169 -0.0363 -0.042 0.0579
Timor-Leste Trinidad and Tobago Turkmenistan United Kingdom
Predicted 0.695 0.9322 0.793 1.0207
cvpred 0.694 0.9248 0.780 1.0232
LTR 0.583 0.9880 0.996 0.9900
CV residual -0.111 0.0632 0.216 -0.0332
Yemen, Rep.
Predicted 0.7265
cvpred 0.7306
LTR 0.6390
CV residual -0.0916
Sum of squares = 0.18 Mean square = 0.01 n = 24
fold 3
Observations in test set: 24
Argentina Armenia Bosnia and Herzegovina Canada Chad
Predicted 0.9528 0.9737 0.9535 0.96659 0.594
cvpred 0.9513 0.9639 0.9501 0.98305 0.620
LTR 0.9780 0.9960 0.9790 0.99000 0.345
CV residual 0.0267 0.0321 0.0289 0.00695 -0.275
Croatia Dominican Republic Finland France Guatemala Iraq
Predicted 0.98260 0.89483 1.0460 0.98818 0.873 0.8532
cvpred 0.98602 0.89374 1.0493 0.99845 0.862 0.8573
LTR 0.98800 0.89500 0.9990 0.99000 0.752 0.7820
CV residual 0.00198 0.00126 -0.0503 -0.00845 -0.110 -0.0753
Kazakhstan Mexico Netherlands Panama Paraguay Puerto Rico
Predicted 0.9134 0.9056 1.0038 0.9819 0.8612 0.9833
cvpred 0.9181 0.9106 1.0129 0.9651 0.8566 0.9982
LTR 0.9970 0.9310 0.9900 0.9410 0.9390 0.9040
CV residual 0.0789 0.0204 -0.0229 -0.0241 0.0824 -0.0942
Russian Federation Singapore Sudan Suriname Uganda Uruguay
Predicted 0.9645 1.0185 0.7288 0.95836 0.612 0.98017
cvpred 0.9644 1.0205 0.7417 0.95248 0.617 0.97914
LTR 0.9960 0.9590 0.7110 0.94700 0.732 0.98100
CV residual 0.0316 -0.0615 -0.0307 -0.00548 0.115 0.00186
Vietnam
Predicted 0.8844
cvpred 0.8623
LTR 0.9320
CV residual 0.0697
Sum of squares = 0.15 Mean square = 0.01 n = 24
fold 4
Observations in test set: 24
Antigua and Barbuda Aruba Bangladesh China Colombia
Predicted 1.0237 0.98234 0.739 0.8355 0.9131
cvpred 1.0079 0.97725 0.760 0.8503 0.9145
LTR 0.9900 0.96800 0.568 0.9430 0.9340
CV residual -0.0179 -0.00925 -0.192 0.0927 0.0195
Costa Rica Gabon Greece Japan Jordan Latvia Macedonia, FYR
Predicted 0.8920 0.8721 1.0101 0.9990 0.9113 0.9812 0.9934
cvpred 0.9048 0.8699 1.0075 1.0015 0.9109 0.9759 0.9857
LTR 0.9620 0.8840 0.9720 0.9900 0.9260 0.9980 0.9730
CV residual 0.0572 0.0141 -0.0355 -0.0115 0.0151 0.0221 -0.0127
Malaysia Mali Namibia Nepal Papua New Guinea South Africa
Predicted 0.9140 0.647 0.9229 0.675 0.6694 0.8518
cvpred 0.9141 0.667 0.9174 0.706 0.7006 0.8467
LTR 0.9310 0.311 0.8880 0.603 0.6060 0.9300
CV residual 0.0169 -0.356 -0.0294 -0.103 -0.0946 0.0833
Spain Syrian Arab Republic Tajikistan Ukraine United States
Predicted 1.0417 0.82766 0.794 0.9184 0.97991
cvpred 1.0367 0.84356 0.801 0.9128 0.98249
LTR 0.9770 0.83400 0.997 0.9970 0.99000
CV residual -0.0597 -0.00956 0.196 0.0842 0.00751
Vanuatu
Predicted 0.80602
cvpred 0.81906
LTR 0.82600
CV residual 0.00694
Sum of squares = 0.26 Mean square = 0.01 n = 24
Overall (Sum over all 24 folds)
ms
0.00931
Analysis of Variance Table
Response: LTR
Df Sum Sq Mean Sq F value Pr(>F)
GDP 1 0.932 0.932 118.89 < 2e-16
UNEMP 1 0.006 0.006 0.71 0.4002
URBGR 1 0.158 0.158 20.19 2.1e-05
MOBILE 1 0.176 0.176 22.45 8.2e-06
INTERNET 1 0.003 0.003 0.34 0.5624
LEXP 1 0.077 0.077 9.79 0.0024
Residuals 88 0.689 0.008
Warning:
As there is >1 explanatory variable, cross-validation predicted values for
a fold are not a linear function of corresponding overall predicted
values. Lines that are shown for the different folds are approximate
fold 1
Observations in test set: 23
Brazil Brunei Darussalam Congo, Dem. Rep. Cyprus El Salvador
Predicted 0.9411 0.96290 0.598 0.969 0.920
cvpred 0.9441 0.95637 0.468 0.955 0.946
LTR 0.9040 0.95200 0.668 0.983 0.845
CV residual -0.0401 -0.00437 0.200 0.028 -0.101
Equatorial Guinea Georgia Germany Ghana Honduras Italy
Predicted 0.786 0.9148 1.0207 0.7515 0.889 1.0550
cvpred 0.728 0.9148 1.0307 0.7436 0.910 1.0652
LTR 0.939 0.9970 0.9900 0.6730 0.848 0.9890
CV residual 0.211 0.0822 -0.0407 -0.0706 -0.062 -0.0762
Jamaica Kenya Lithuania Montenegro Qatar Romania Samoa
Predicted 0.951 0.789 1.0178 1.0296 0.867 0.94973 0.816
cvpred 0.971 0.721 1.0469 1.0546 0.783 0.97527 0.742
LTR 0.866 0.874 0.9970 0.9840 0.963 0.97700 0.988
CV residual -0.105 0.153 -0.0499 -0.0706 0.180 0.00173 0.246
Slovenia Sri Lanka United Arab Emirates Uzbekistan Zambia
Predicted 0.98437 0.8820 0.9115 0.787 0.6697
cvpred 0.98779 0.8979 0.8457 0.803 0.6247
LTR 0.99700 0.9120 0.9000 0.994 0.7120
CV residual 0.00921 0.0141 0.0543 0.191 0.0873
Sum of squares = 0.3 Mean square = 0.01 n = 23
fold 2
Observations in test set: 24
Angola Bahrain Botswana Ecuador Egypt, Arab Rep. Estonia
Predicted 0.71097 0.9193 0.8144 0.9027 0.862 0.990179
cvpred 0.70923 0.9253 0.7883 0.9018 0.861 0.998903
LTR 0.70100 0.9190 0.8450 0.9190 0.720 0.998000
CV residual -0.00823 -0.0063 0.0567 0.0172 -0.141 -0.000903
Hungary India Moldova Mongolia Mozambique Nigeria Poland
Predicted 0.9632 0.7702 0.837 0.822 0.591 0.6938 0.9801
cvpred 0.9657 0.7609 0.835 0.811 0.587 0.6953 0.9808
LTR 0.9900 0.7400 0.985 0.974 0.561 0.6130 0.9950
CV residual 0.0243 -0.0209 0.150 0.163 -0.026 -0.0823 0.0142
Portugal Saudi Arabia Serbia Sweden Switzerland Tanzania
Predicted 0.9981 1.013 0.974830 1.0121 1.0256 0.6679
cvpred 1.0004 1.009 0.978462 1.0221 1.0301 0.6706
LTR 0.9520 0.866 0.979000 0.9900 0.9900 0.7320
CV residual -0.0484 -0.143 0.000538 -0.0321 -0.0401 0.0614
Timor-Leste Trinidad and Tobago Turkmenistan United Kingdom
Predicted 0.697 0.9308 0.804 1.012
cvpred 0.695 0.9241 0.785 1.019
LTR 0.583 0.9880 0.996 0.990
CV residual -0.112 0.0639 0.211 -0.029
Yemen, Rep.
Predicted 0.7263
cvpred 0.7302
LTR 0.6390
CV residual -0.0912
Sum of squares = 0.18 Mean square = 0.01 n = 24
fold 3
Observations in test set: 24
Argentina Armenia Bosnia and Herzegovina Canada Chad Croatia
Predicted 0.9519 0.9782 0.9482 0.9616 0.588 0.98020
cvpred 0.9504 0.9742 0.9418 0.9717 0.607 0.98192
LTR 0.9780 0.9960 0.9790 0.9900 0.345 0.98800
CV residual 0.0276 0.0218 0.0372 0.0183 -0.262 0.00608
Dominican Republic Finland France Guatemala Iraq Kazakhstan
Predicted 0.89786 1.037 0.98271 0.882 0.868 0.9165
cvpred 0.89934 1.033 0.98722 0.878 0.883 0.9237
LTR 0.89500 0.999 0.99000 0.752 0.782 0.9970
CV residual -0.00434 -0.034 0.00278 -0.126 -0.101 0.0733
Mexico Netherlands Panama Paraguay Puerto Rico
Predicted 0.91314 0.99296 0.9843 0.8658 0.992
cvpred 0.92305 0.99259 0.9715 0.8654 1.012
LTR 0.93100 0.99000 0.9410 0.9390 0.904
CV residual 0.00795 -0.00259 -0.0305 0.0736 -0.108
Russian Federation Singapore Sudan Suriname Uganda Uruguay
Predicted 0.9632 1.0177 0.7256 0.9624 0.602 0.98160
cvpred 0.9634 1.0185 0.7348 0.9611 0.598 0.98224
LTR 0.9960 0.9590 0.7110 0.9470 0.732 0.98100
CV residual 0.0326 -0.0595 -0.0238 -0.0141 0.134 -0.00124
Vietnam
Predicted 0.8795
cvpred 0.8562
LTR 0.9320
CV residual 0.0758
Sum of squares = 0.15 Mean square = 0.01 n = 24
fold 4
Observations in test set: 24
Antigua and Barbuda Aruba Bangladesh China Colombia
Predicted 1.008506 0.97944 0.741 0.8362 0.9148
cvpred 0.989708 0.97329 0.763 0.8516 0.9167
LTR 0.990000 0.96800 0.568 0.9430 0.9340
CV residual 0.000292 -0.00529 -0.195 0.0914 0.0173
Costa Rica Gabon Greece Japan Jordan Latvia
Predicted 0.8976 0.88616 1.0202 0.99525 0.91584 0.9706
cvpred 0.9121 0.88696 1.0198 0.99737 0.91672 0.9637
LTR 0.9620 0.88400 0.9720 0.99000 0.92600 0.9980
CV residual 0.0499 -0.00296 -0.0478 -0.00737 0.00928 0.0343
Macedonia, FYR Malaysia Mali Namibia Nepal Papua New Guinea
Predicted 0.98826 0.9074 0.642 0.9354 0.673 0.6729
cvpred 0.98159 0.9062 0.662 0.9367 0.703 0.7045
LTR 0.97300 0.9310 0.311 0.8880 0.603 0.6060
CV residual -0.00859 0.0248 -0.351 -0.0487 -0.100 -0.0985
South Africa Spain Syrian Arab Republic Tajikistan Ukraine
Predicted 0.8526 1.043 0.8329 0.791 0.9201
cvpred 0.8485 1.040 0.8505 0.796 0.9136
LTR 0.9300 0.977 0.8340 0.997 0.9970
CV residual 0.0815 -0.063 -0.0165 0.201 0.0834
United States Vanuatu
Predicted 0.9771 0.8154
cvpred 0.9799 0.8299
LTR 0.9900 0.8260
CV residual 0.0101 -0.0039
Sum of squares = 0.26 Mean square = 0.01 n = 24
Overall (Sum over all 24 folds)
ms
0.00939
Analysis of Variance Table
Response: LTR
Df Sum Sq Mean Sq F value Pr(>F)
GDP 1 0.932 0.932 119.54 < 2e-16
UNEMP 1 0.006 0.006 0.72 0.3989
URBGR 1 0.158 0.158 20.30 2.0e-05
MOBILE 1 0.176 0.176 22.57 7.7e-06
LEXP 1 0.075 0.075 9.66 0.0025
Residuals 89 0.694 0.008
Warning:
As there is >1 explanatory variable, cross-validation predicted values for
a fold are not a linear function of corresponding overall predicted
values. Lines that are shown for the different folds are approximate
fold 1
Observations in test set: 23
Angola Aruba Bangladesh Brunei Darussalam Chad Ecuador
Predicted 0.7081 0.982 0.739 0.9584 0.594 0.8987
cvpred 0.6707 0.994 0.756 0.9415 0.620 0.8858
LTR 0.7010 0.968 0.568 0.9520 0.345 0.9190
CV residual 0.0303 -0.026 -0.188 0.0105 -0.275 0.0332
Equatorial Guinea Georgia Germany Iraq Kenya Montenegro
Predicted 0.772 0.913 1.0281 0.8532 0.792 1.0265
cvpred 0.758 0.923 1.0388 0.8435 0.746 1.0249
LTR 0.939 0.997 0.9900 0.7820 0.874 0.9840
CV residual 0.181 0.074 -0.0488 -0.0615 0.128 -0.0409
Paraguay Qatar Romania Saudi Arabia Slovenia
Predicted 0.8612 0.871 0.9492 1.007 0.98938
cvpred 0.8529 0.687 0.9788 0.981 1.00213
LTR 0.9390 0.963 0.9770 0.866 0.99700
CV residual 0.0861 0.276 -0.0018 -0.115 -0.00513
Syrian Arab Republic Uganda Ukraine United Arab Emirates
Predicted 0.8277 0.612 0.9184 0.913
cvpred 0.8181 0.588 0.9531 0.758
LTR 0.8340 0.732 0.9970 0.900
CV residual 0.0159 0.144 0.0439 0.142
Vanuatu Vietnam
Predicted 0.8060 0.8844
cvpred 0.7919 0.8683
LTR 0.8260 0.9320
CV residual 0.0341 0.0637
Sum of squares = 0.32 Mean square = 0.01 n = 23
fold 2
Observations in test set: 24
Bahrain Brazil China Colombia Croatia Cyprus Estonia Gabon
Predicted 0.91953 0.937 0.835 0.9131 0.983 0.9643 1.00e+00 0.8721
cvpred 0.92459 0.927 0.819 0.9072 0.974 0.9491 9.98e-01 0.8727
LTR 0.91900 0.904 0.943 0.9340 0.988 0.9830 9.98e-01 0.8840
CV residual -0.00559 -0.023 0.124 0.0268 0.014 0.0339 8.93e-05 0.0113
Honduras Jamaica Kazakhstan Lithuania Moldova Netherlands
Predicted 0.8821 0.9469 0.9134 1.0253 0.844 1.0038
cvpred 0.8891 0.9431 0.9077 1.0237 0.837 0.9918
LTR 0.8480 0.8660 0.9970 0.9970 0.985 0.9900
CV residual -0.0411 -0.0771 0.0893 -0.0267 0.148 -0.0018
Papua New Guinea Samoa Singapore Tanzania Trinidad and Tobago
Predicted 0.6694 0.803 1.0185 0.6756 0.9322
cvpred 0.6246 0.753 1.0158 0.6618 0.9339
LTR 0.6060 0.988 0.9590 0.7320 0.9880
CV residual -0.0186 0.235 -0.0568 0.0702 0.0541
Turkmenistan United Kingdom United States Yemen, Rep. Zambia
Predicted 0.793 1.0207 0.9799 0.7265 0.6737
cvpred 0.768 1.0146 0.9632 0.7099 0.6531
LTR 0.996 0.9900 0.9900 0.6390 0.7120
CV residual 0.228 -0.0246 0.0268 -0.0709 0.0589
Sum of squares = 0.18 Mean square = 0.01 n = 24
fold 3
Observations in test set: 24
Antigua and Barbuda Argentina Bosnia and Herzegovina Botswana
Predicted 1.0237 0.9528 0.9535 0.8096
cvpred 1.0234 0.9588 0.9559 0.8135
LTR 0.9900 0.9780 0.9790 0.8450
CV residual -0.0334 0.0192 0.0231 0.0315
Dominican Republic Egypt, Arab Rep. Finland Ghana India
Predicted 0.8948 0.865 1.0460 0.751 0.7678
cvpred 0.9059 0.878 1.0446 0.773 0.7898
LTR 0.8950 0.720 0.9990 0.673 0.7400
CV residual -0.0109 -0.158 -0.0456 -0.100 -0.0498
Italy Japan Malaysia Mali Nepal Panama Portugal
Predicted 1.0478 0.9990 0.91402 0.647 0.675 0.9819 0.9946
cvpred 1.0476 1.0034 0.92707 0.676 0.706 0.9904 0.9975
LTR 0.9890 0.9900 0.93100 0.311 0.603 0.9410 0.9520
CV residual -0.0586 -0.0134 0.00393 -0.365 -0.103 -0.0494 -0.0455
Russian Federation Serbia Spain Suriname Switzerland
Predicted 0.9645 0.9755 1.0417 0.9584 1.0296
cvpred 0.9669 0.9768 1.0385 0.9634 1.0312
LTR 0.9960 0.9790 0.9770 0.9470 0.9900
CV residual 0.0291 0.0022 -0.0615 -0.0164 -0.0412
Timor-Leste Uruguay Uzbekistan
Predicted 0.695 0.98017 0.790
cvpred 0.725 0.98468 0.813
LTR 0.583 0.98100 0.994
CV residual -0.142 -0.00368 0.181
Sum of squares = 0.25 Mean square = 0.01 n = 24
fold 4
Observations in test set: 24
Armenia Canada Congo, Dem. Rep. Costa Rica El Salvador
Predicted 0.9737 0.9666 0.6061 0.8920 0.9125
cvpred 0.9682 0.9749 0.6164 0.8896 0.9022
LTR 0.9960 0.9900 0.6680 0.9620 0.8450
CV residual 0.0278 0.0151 0.0516 0.0724 -0.0572
France Greece Guatemala Hungary Jordan Latvia
Predicted 0.98818 1.0101 0.873 0.9714 0.9113 0.9812
cvpred 0.99525 1.0151 0.861 0.9714 0.9067 0.9844
LTR 0.99000 0.9720 0.752 0.9900 0.9260 0.9980
CV residual -0.00525 -0.0431 -0.109 0.0186 0.0193 0.0136
Macedonia, FYR Mexico Mongolia Mozambique Namibia Nigeria
Predicted 0.9934 0.9056 0.817 0.6020 0.9229 0.7050
cvpred 0.9986 0.9018 0.805 0.5928 0.9443 0.7052
LTR 0.9730 0.9310 0.974 0.5610 0.8880 0.6130
CV residual -0.0256 0.0292 0.169 -0.0318 -0.0563 -0.0922
Poland Puerto Rico South Africa Sri Lanka Sudan Sweden
Predicted 0.9864 0.9833 0.8518 0.8743 0.7288 1.021
cvpred 0.9844 0.9917 0.8604 0.8617 0.7237 1.028
LTR 0.9950 0.9040 0.9300 0.9120 0.7110 0.990
CV residual 0.0106 -0.0877 0.0696 0.0503 -0.0127 -0.038
Tajikistan
Predicted 0.794
cvpred 0.774
LTR 0.997
CV residual 0.223
Sum of squares = 0.14 Mean square = 0.01 n = 24
Overall (Sum over all 24 folds)
ms
0.00943
Analysis of Variance Table
Response: LTR
Df Sum Sq Mean Sq F value Pr(>F)
GDP 1 0.932 0.932 118.89 < 2e-16
UNEMP 1 0.006 0.006 0.71 0.4002
URBGR 1 0.158 0.158 20.19 2.1e-05
MOBILE 1 0.176 0.176 22.45 8.2e-06
INTERNET 1 0.003 0.003 0.34 0.5624
LEXP 1 0.077 0.077 9.79 0.0024
Residuals 88 0.689 0.008
Warning:
As there is >1 explanatory variable, cross-validation predicted values for
a fold are not a linear function of corresponding overall predicted
values. Lines that are shown for the different folds are approximate
fold 1
Observations in test set: 23
Angola Aruba Bangladesh Brunei Darussalam Chad Ecuador
Predicted 0.7110 0.9794 0.741 0.96290 0.588 0.9027
cvpred 0.6761 0.9917 0.757 0.94749 0.614 0.8902
LTR 0.7010 0.9680 0.568 0.95200 0.345 0.9190
CV residual 0.0249 -0.0237 -0.189 0.00451 -0.269 0.0288
Equatorial Guinea Georgia Germany Iraq Kenya Montenegro
Predicted 0.786 0.9148 1.0207 0.8682 0.789 1.0296
cvpred 0.778 0.9254 1.0306 0.8627 0.742 1.0292
LTR 0.939 0.9970 0.9900 0.7820 0.874 0.9840
CV residual 0.161 0.0716 -0.0406 -0.0807 0.132 -0.0452
Paraguay Qatar Romania Saudi Arabia Slovenia
Predicted 0.8658 0.867 0.94973 1.013 0.984373
cvpred 0.8584 0.679 0.98061 0.989 0.996675
LTR 0.9390 0.963 0.97700 0.866 0.997000
CV residual 0.0806 0.284 -0.00361 -0.123 0.000325
Syrian Arab Republic Uganda Ukraine United Arab Emirates
Predicted 0.8329 0.602 0.9201 0.912
cvpred 0.8238 0.575 0.9561 0.754
LTR 0.8340 0.732 0.9970 0.900
CV residual 0.0102 0.157 0.0409 0.146
Vanuatu Vietnam
Predicted 0.8154 0.8795
cvpred 0.8032 0.8605
LTR 0.8260 0.9320
CV residual 0.0228 0.0715
Sum of squares = 0.32 Mean square = 0.01 n = 23
fold 2
Observations in test set: 24
Bahrain Brazil China Colombia Croatia Cyprus Estonia Gabon
Predicted 0.91934 0.9411 0.836 0.9148 0.9802 0.9692 0.99018 0.8862
cvpred 0.92457 0.9271 0.819 0.9072 0.9739 0.9492 0.99763 0.8731
LTR 0.91900 0.9040 0.943 0.9340 0.9880 0.9830 0.99800 0.8840
CV residual -0.00557 -0.0231 0.124 0.0268 0.0141 0.0338 0.00037 0.0109
Honduras Jamaica Kazakhstan Lithuania Moldova Netherlands
Predicted 0.8890 0.9513 0.9165 1.0178 0.837 0.99296
cvpred 0.8893 0.9432 0.9077 1.0235 0.837 0.99154
LTR 0.8480 0.8660 0.9970 0.9970 0.985 0.99000
CV residual -0.0413 -0.0772 0.0893 -0.0265 0.148 -0.00154
Papua New Guinea Samoa Singapore Tanzania Trinidad and Tobago
Predicted 0.6729 0.816 1.0177 0.6679 0.9308
cvpred 0.6247 0.754 1.0158 0.6616 0.9338
LTR 0.6060 0.988 0.9590 0.7320 0.9880
CV residual -0.0187 0.234 -0.0568 0.0704 0.0542
Turkmenistan United Kingdom United States Yemen, Rep. Zambia
Predicted 0.804 1.0115 0.9771 0.726 0.6697
cvpred 0.769 1.0144 0.9632 0.710 0.6531
LTR 0.996 0.9900 0.9900 0.639 0.7120
CV residual 0.227 -0.0244 0.0268 -0.071 0.0589
Sum of squares = 0.18 Mean square = 0.01 n = 24
fold 3
Observations in test set: 24
Antigua and Barbuda Argentina Bosnia and Herzegovina Botswana
Predicted 1.0085 0.9519 0.9482 0.8144
cvpred 1.0109 0.9576 0.9512 0.8178
LTR 0.9900 0.9780 0.9790 0.8450
CV residual -0.0209 0.0204 0.0278 0.0272
Dominican Republic Egypt, Arab Rep. Finland Ghana India
Predicted 0.8979 0.862 1.0368 0.752 0.7702
cvpred 0.9079 0.876 1.0368 0.773 0.7915
LTR 0.8950 0.720 0.9990 0.673 0.7400
CV residual -0.0129 -0.156 -0.0378 -0.100 -0.0515
Italy Japan Malaysia Mali Nepal Panama Portugal
Predicted 1.0550 0.99525 0.90740 0.642 0.673 0.9843 0.9981
cvpred 1.0527 0.99995 0.92144 0.672 0.704 0.9917 0.9998
LTR 0.9890 0.99000 0.93100 0.311 0.603 0.9410 0.9520
CV residual -0.0637 -0.00995 0.00956 -0.361 -0.101 -0.0507 -0.0478
Russian Federation Serbia Spain Suriname Switzerland
Predicted 0.9632 0.97483 1.0433 0.9624 1.0256
cvpred 0.9656 0.97574 1.0392 0.9662 1.0276
LTR 0.9960 0.97900 0.9770 0.9470 0.9900
CV residual 0.0304 0.00326 -0.0622 -0.0192 -0.0376
Timor-Leste Uruguay Uzbekistan
Predicted 0.697 0.9816 0.787
cvpred 0.727 0.9853 0.810
LTR 0.583 0.9810 0.994
CV residual -0.144 -0.0043 0.184
Sum of squares = 0.25 Mean square = 0.01 n = 24
fold 4
Observations in test set: 24
Armenia Canada Congo, Dem. Rep. Costa Rica El Salvador France
Predicted 0.9782 0.9616 0.598 0.8976 0.9197 0.98271
cvpred 0.9782 0.9643 0.593 0.9006 0.9172 0.98479
LTR 0.9960 0.9900 0.668 0.9620 0.8450 0.99000
CV residual 0.0178 0.0257 0.075 0.0614 -0.0722 0.00521
Greece Guatemala Hungary Jordan Latvia Macedonia, FYR Mexico
Predicted 1.0202 0.882 0.9632 0.9158 0.9706 0.988 0.9131
cvpred 1.0342 0.879 0.9561 0.9167 0.9633 0.989 0.9163
LTR 0.9720 0.752 0.9900 0.9260 0.9980 0.973 0.9310
CV residual -0.0622 -0.127 0.0339 0.0093 0.0347 -0.016 0.0147
Mongolia Mozambique Namibia Nigeria Poland Puerto Rico
Predicted 0.822 0.59095 0.9354 0.694 0.9801 0.992
cvpred 0.814 0.56682 0.9647 0.680 0.9732 1.007
LTR 0.974 0.56100 0.8880 0.613 0.9950 0.904
CV residual 0.160 -0.00582 -0.0767 -0.067 0.0218 -0.103
South Africa Sri Lanka Sudan Sweden Tajikistan
Predicted 0.8526 0.8820 0.72559 1.012 0.791
cvpred 0.8575 0.8772 0.71442 1.011 0.770
LTR 0.9300 0.9120 0.71100 0.990 0.997
CV residual 0.0725 0.0348 -0.00342 -0.021 0.227
Sum of squares = 0.14 Mean square = 0.01 n = 24
Overall (Sum over all 24 folds)
ms
0.00953
Analysis of Variance Table
Response: LTR
Df Sum Sq Mean Sq F value Pr(>F)
GDP 1 0.932 0.932 119.54 < 2e-16
UNEMP 1 0.006 0.006 0.72 0.3989
URBGR 1 0.158 0.158 20.30 2.0e-05
MOBILE 1 0.176 0.176 22.57 7.7e-06
LEXP 1 0.075 0.075 9.66 0.0025
Residuals 89 0.694 0.008
Warning:
As there is >1 explanatory variable, cross-validation predicted values for
a fold are not a linear function of corresponding overall predicted
values. Lines that are shown for the different folds are approximate
fold 1
Observations in test set: 23
Antigua and Barbuda Armenia Botswana China Costa Rica
Predicted 1.0237 0.9737 0.810 0.835 0.8920
cvpred 1.0186 0.9803 0.754 0.841 0.9035
LTR 0.9900 0.9960 0.845 0.943 0.9620
CV residual -0.0286 0.0157 0.091 0.102 0.0585
Equatorial Guinea Finland France Georgia Greece Honduras
Predicted 0.772 1.0460 0.98818 0.913 1.0101 0.8821
cvpred 0.727 1.0424 0.99237 0.921 1.0145 0.8857
LTR 0.939 0.9990 0.99000 0.997 0.9720 0.8480
CV residual 0.212 -0.0434 -0.00237 0.076 -0.0425 -0.0377
Hungary India Iraq Jamaica Jordan Kazakhstan Latvia
Predicted 0.9714 0.7678 0.8532 0.947 0.9113 0.913 0.9812
cvpred 0.9658 0.7595 0.8498 0.945 0.9151 0.895 0.9781
LTR 0.9900 0.7400 0.7820 0.866 0.9260 0.997 0.9980
CV residual 0.0242 -0.0195 -0.0678 -0.079 0.0109 0.102 0.0199
Macedonia, FYR Nepal Singapore Sudan Tajikistan
Predicted 0.993 0.6750 1.0185 0.72881 0.794
cvpred 1.007 0.6788 1.0179 0.71863 0.791
LTR 0.973 0.6030 0.9590 0.71100 0.997
CV residual -0.034 -0.0758 -0.0589 -0.00763 0.206
Sum of squares = 0.15 Mean square = 0.01 n = 23
fold 2
Observations in test set: 24
Angola Bangladesh Brazil Brunei Darussalam Canada Chad
Predicted 0.7081 0.739 0.9375 0.9584 0.9666 0.594
cvpred 0.7416 0.749 0.9465 0.9739 1.0013 0.639
LTR 0.7010 0.568 0.9040 0.9520 0.9900 0.345
CV residual -0.0406 -0.181 -0.0425 -0.0219 -0.0113 -0.294
Cyprus Ghana Guatemala Italy Moldova Papua New Guinea
Predicted 0.96431 0.7515 0.873 1.0478 0.844 0.669
cvpred 0.98513 0.7529 0.856 1.0492 0.840 0.715
LTR 0.98300 0.6730 0.752 0.9890 0.985 0.606
CV residual -0.00213 -0.0799 -0.104 -0.0602 0.145 -0.109
Poland Portugal Puerto Rico Romania Slovenia Spain
Predicted 0.98637 0.9946 0.983 0.9492 0.98938 1.0417
cvpred 0.99041 1.0039 1.013 0.9533 1.00557 1.0537
LTR 0.99500 0.9520 0.904 0.9770 0.99700 0.9770
CV residual 0.00459 -0.0519 -0.109 0.0237 -0.00857 -0.0767
Switzerland Tanzania Trinidad and Tobago United States
Predicted 1.0296 0.6756 0.9322 0.9799
cvpred 1.0482 0.6826 0.9322 1.0079
LTR 0.9900 0.7320 0.9880 0.9900
CV residual -0.0582 0.0494 0.0558 -0.0179
Uzbekistan Vietnam
Predicted 0.790 0.8844
cvpred 0.789 0.8542
LTR 0.994 0.9320
CV residual 0.205 0.0778
Sum of squares = 0.26 Mean square = 0.01 n = 24
fold 3
Observations in test set: 24
Bahrain Bosnia and Herzegovina Colombia Dominican Republic
Predicted 0.920 0.9535 0.9131 0.89483
cvpred 0.941 0.9471 0.9192 0.90085
LTR 0.919 0.9790 0.9340 0.89500
CV residual -0.022 0.0319 0.0148 -0.00585
Egypt, Arab Rep. Estonia Gabon Germany Japan Lithuania
Predicted 0.865 1.00116 0.8721 1.0281 0.99898 1.0253
cvpred 0.873 1.00627 0.8963 1.0252 0.98445 1.0362
LTR 0.720 0.99800 0.8840 0.9900 0.99000 0.9970
CV residual -0.153 -0.00827 -0.0123 -0.0352 0.00555 -0.0392
Malaysia Montenegro Mozambique Namibia Nigeria Panama Samoa
Predicted 0.914018 1.0265 0.602 0.923 0.705 0.982 0.803
cvpred 0.931984 1.0554 0.599 0.937 0.723 1.018 0.741
LTR 0.931000 0.9840 0.561 0.888 0.613 0.941 0.988
CV residual -0.000984 -0.0714 -0.038 -0.049 -0.110 -0.077 0.247
Saudi Arabia Suriname Sweden Timor-Leste Ukraine Uruguay
Predicted 1.007 0.9584 1.021 0.695 0.9184 0.98017
cvpred 1.038 0.9912 1.016 0.690 0.9343 0.99024
LTR 0.866 0.9470 0.990 0.583 0.9970 0.98100
CV residual -0.172 -0.0442 -0.026 -0.107 0.0627 -0.00924
Zambia
Predicted 0.6737
cvpred 0.6765
LTR 0.7120
CV residual 0.0355
Sum of squares = 0.17 Mean square = 0.01 n = 24
fold 4
Observations in test set: 24
Argentina Aruba Congo, Dem. Rep. Croatia Ecuador El Salvador
Predicted 0.9528 0.9823 0.6061 0.98260 0.8987 0.9125
cvpred 0.9518 0.9852 0.5772 0.98444 0.8855 0.9121
LTR 0.9780 0.9680 0.6680 0.98800 0.9190 0.8450
CV residual 0.0262 -0.0172 0.0908 0.00356 0.0335 -0.0671
Kenya Mali Mexico Mongolia Netherlands Paraguay Qatar
Predicted 0.792 0.647 0.9056 0.817 1.00377 0.861 0.871
cvpred 0.760 0.630 0.8986 0.809 0.99568 0.850 0.779
LTR 0.874 0.311 0.9310 0.974 0.99000 0.939 0.963
CV residual 0.114 -0.319 0.0324 0.165 -0.00568 0.089 0.184
Russian Federation Serbia South Africa Sri Lanka
Predicted 0.9645 0.97553 0.8518 0.874
cvpred 0.9718 0.97626 0.8471 0.878
LTR 0.9960 0.97900 0.9300 0.912
CV residual 0.0242 0.00274 0.0829 0.034
Syrian Arab Republic Turkmenistan Uganda United Arab Emirates
Predicted 0.8277 0.793 0.612 0.9129
cvpred 0.8102 0.796 0.588 0.8355
LTR 0.8340 0.996 0.732 0.9000
CV residual 0.0238 0.200 0.144 0.0645
United Kingdom Vanuatu Yemen, Rep.
Predicted 1.0207 0.8060 0.7265
cvpred 1.0133 0.7901 0.7056
LTR 0.9900 0.8260 0.6390
CV residual -0.0233 0.0359 -0.0666
Sum of squares = 0.28 Mean square = 0.01 n = 24
Overall (Sum over all 24 folds)
ms
0.009
Analysis of Variance Table
Response: LTR
Df Sum Sq Mean Sq F value Pr(>F)
GDP 1 0.932 0.932 118.89 < 2e-16
UNEMP 1 0.006 0.006 0.71 0.4002
URBGR 1 0.158 0.158 20.19 2.1e-05
MOBILE 1 0.176 0.176 22.45 8.2e-06
INTERNET 1 0.003 0.003 0.34 0.5624
LEXP 1 0.077 0.077 9.79 0.0024
Residuals 88 0.689 0.008
Warning:
As there is >1 explanatory variable, cross-validation predicted values for
a fold are not a linear function of corresponding overall predicted
values. Lines that are shown for the different folds are approximate
fold 1
Observations in test set: 23
Antigua and Barbuda Armenia Botswana China Costa Rica
Predicted 1.009 0.9782 0.8144 0.836 0.8976
cvpred 1.009 0.9822 0.7592 0.841 0.9066
LTR 0.990 0.9960 0.8450 0.943 0.9620
CV residual -0.019 0.0138 0.0858 0.102 0.0554
Equatorial Guinea Finland France Georgia Greece Honduras
Predicted 0.786 1.0368 0.98271 0.9148 1.0202 0.8890
cvpred 0.738 1.0366 0.98893 0.9215 1.0204 0.8895
LTR 0.939 0.9990 0.99000 0.9970 0.9720 0.8480
CV residual 0.201 -0.0376 0.00107 0.0755 -0.0484 -0.0415
Hungary India Iraq Jamaica Jordan Kazakhstan Latvia
Predicted 0.9632 0.7702 0.8682 0.9513 0.91584 0.9165 0.9706
cvpred 0.9608 0.7612 0.8592 0.9473 0.91757 0.8976 0.9713
LTR 0.9900 0.7400 0.7820 0.8660 0.92600 0.9970 0.9980
CV residual 0.0292 -0.0212 -0.0772 -0.0813 0.00843 0.0994 0.0267
Macedonia, FYR Nepal Singapore Sudan Tajikistan
Predicted 0.9883 0.6726 1.0177 0.72559 0.791
cvpred 1.0029 0.6774 1.0173 0.71724 0.789
LTR 0.9730 0.6030 0.9590 0.71100 0.997
CV residual -0.0299 -0.0744 -0.0583 -0.00624 0.208
Sum of squares = 0.15 Mean square = 0.01 n = 23
fold 2
Observations in test set: 24
Angola Bangladesh Brazil Brunei Darussalam Canada Chad
Predicted 0.7110 0.741 0.9411 0.9629 0.96157 0.588
cvpred 0.7488 0.751 0.9556 0.9862 0.99221 0.622
LTR 0.7010 0.568 0.9040 0.9520 0.99000 0.345
CV residual -0.0478 -0.183 -0.0516 -0.0342 -0.00221 -0.277
Cyprus Ghana Guatemala Italy Moldova Papua New Guinea
Predicted 0.9692 0.7515 0.882 1.0550 0.837 0.673
cvpred 0.9987 0.7507 0.874 1.0683 0.820 0.722
LTR 0.9830 0.6730 0.752 0.9890 0.985 0.606
CV residual -0.0157 -0.0777 -0.122 -0.0793 0.165 -0.116
Poland Portugal Puerto Rico Romania Slovenia Spain
Predicted 0.980 0.9981 0.992 0.9497 0.98437 1.0433
cvpred 0.976 1.0139 1.037 0.9544 0.99512 1.0604
LTR 0.995 0.9520 0.904 0.9770 0.99700 0.9770
CV residual 0.019 -0.0619 -0.133 0.0226 0.00188 -0.0834
Switzerland Tanzania Trinidad and Tobago United States
Predicted 1.0256 0.6679 0.931 0.977
cvpred 1.0414 0.6612 0.929 1.004
LTR 0.9900 0.7320 0.988 0.990
CV residual -0.0514 0.0708 0.059 -0.014
Uzbekistan Vietnam
Predicted 0.787 0.8795
cvpred 0.779 0.8395
LTR 0.994 0.9320
CV residual 0.215 0.0925
Sum of squares = 0.28 Mean square = 0.01 n = 24
fold 3
Observations in test set: 24
Bahrain Bosnia and Herzegovina Colombia Dominican Republic
Predicted 0.919 0.9482 0.9148 0.89786
cvpred 0.941 0.9461 0.9198 0.90194
LTR 0.919 0.9790 0.9340 0.89500
CV residual -0.022 0.0329 0.0142 -0.00694
Egypt, Arab Rep. Estonia Gabon Germany Japan Lithuania
Predicted 0.862 0.99018 0.8862 1.0207 0.99525 1.0178
cvpred 0.872 1.00283 0.9009 1.0226 0.98305 1.0337
LTR 0.720 0.99800 0.8840 0.9900 0.99000 0.9970
CV residual -0.152 -0.00483 -0.0169 -0.0326 0.00695 -0.0367
Malaysia Montenegro Mozambique Namibia Nigeria Panama Samoa
Predicted 0.90740 1.0296 0.5909 0.9354 0.694 0.9843 0.816
cvpred 0.92966 1.0568 0.5951 0.9425 0.719 1.0189 0.745
LTR 0.93100 0.9840 0.5610 0.8880 0.613 0.9410 0.988
CV residual 0.00134 -0.0728 -0.0341 -0.0545 -0.106 -0.0779 0.243
Saudi Arabia Suriname Sweden Timor-Leste Ukraine Uruguay
Predicted 1.013 0.9624 1.012 0.697 0.9201 0.98160
cvpred 1.040 0.9924 1.013 0.690 0.9346 0.99054
LTR 0.866 0.9470 0.990 0.583 0.9970 0.98100
CV residual -0.174 -0.0454 -0.023 -0.107 0.0624 -0.00954
Zambia
Predicted 0.670
cvpred 0.675
LTR 0.712
CV residual 0.037
Sum of squares = 0.16 Mean square = 0.01 n = 24
fold 4
Observations in test set: 24
Argentina Aruba Congo, Dem. Rep. Croatia Ecuador El Salvador
Predicted 0.952 0.9794 0.5975 0.98020 0.9027 0.9197
cvpred 0.952 0.9845 0.5682 0.98371 0.8879 0.9171
LTR 0.978 0.9680 0.6680 0.98800 0.9190 0.8450
CV residual 0.026 -0.0165 0.0998 0.00429 0.0311 -0.0721
Kenya Mali Mexico Mongolia Netherlands Paraguay Qatar
Predicted 0.789 0.642 0.9131 0.822 0.992957 0.8658 0.867
cvpred 0.755 0.627 0.9032 0.812 0.989663 0.8529 0.770
LTR 0.874 0.311 0.9310 0.974 0.990000 0.9390 0.963
CV residual 0.119 -0.316 0.0278 0.162 0.000337 0.0861 0.193
Russian Federation Serbia South Africa Sri Lanka
Predicted 0.9632 0.97483 0.8526 0.8820
cvpred 0.9724 0.97615 0.8466 0.8837
LTR 0.9960 0.97900 0.9300 0.9120
CV residual 0.0236 0.00285 0.0834 0.0283
Syrian Arab Republic Turkmenistan Uganda United Arab Emirates
Predicted 0.8329 0.804 0.602 0.9115
cvpred 0.8126 0.804 0.581 0.8292
LTR 0.8340 0.996 0.732 0.9000
CV residual 0.0214 0.192 0.151 0.0708
United Kingdom Vanuatu Yemen, Rep.
Predicted 1.0115 0.8154 0.7263
cvpred 1.0082 0.7954 0.7042
LTR 0.9900 0.8260 0.6390
CV residual -0.0182 0.0306 -0.0652
Sum of squares = 0.28 Mean square = 0.01 n = 24
Overall (Sum over all 24 folds)
ms
0.00922
par(mfrow=c(1,1))
# Compare the mean squared errors for prediction
seed <- round(runif(1, min=0, max=100))
ms.g <- CVlm(df=ltrdata10,
form.lm=g.step,
m=4,
seed=seed,
printit=T,
plotit=F)
Analysis of Variance Table
Response: LTR
Df Sum Sq Mean Sq F value Pr(>F)
GDP 1 0.932 0.932 119.54 < 2e-16
UNEMP 1 0.006 0.006 0.72 0.3989
URBGR 1 0.158 0.158 20.30 2.0e-05
MOBILE 1 0.176 0.176 22.57 7.7e-06
LEXP 1 0.075 0.075 9.66 0.0025
Residuals 89 0.694 0.008
fold 1
Observations in test set: 23
Antigua and Barbuda Aruba Bosnia and Herzegovina
Predicted 1.0237 0.9823 0.9535
cvpred 1.0235 0.9948 0.9307
LTR 0.9900 0.9680 0.9790
CV residual -0.0335 -0.0268 0.0483
Congo, Dem. Rep. Finland France Georgia Honduras India
Predicted 0.606 1.0460 0.9882 0.9128 0.8821 0.7678
cvpred 0.552 1.0538 0.9962 0.9048 0.8849 0.7812
LTR 0.668 0.9990 0.9900 0.9970 0.8480 0.7400
CV residual 0.116 -0.0548 -0.0062 0.0922 -0.0369 -0.0412
Jamaica Jordan Kazakhstan Kenya Latvia Lithuania
Predicted 0.9469 0.9113 0.9134 0.792 0.9812 1.0253
cvpred 0.9469 0.9069 0.9253 0.745 0.9767 1.0208
LTR 0.8660 0.9260 0.9970 0.874 0.9980 0.9970
CV residual -0.0809 0.0191 0.0717 0.129 0.0213 -0.0238
Macedonia, FYR Nepal Puerto Rico Sri Lanka Suriname
Predicted 0.993 0.6750 0.9833 0.8743 0.9584
cvpred 0.963 0.6903 0.9853 0.8848 0.9624
LTR 0.973 0.6030 0.9040 0.9120 0.9470
CV residual 0.010 -0.0873 -0.0813 0.0272 -0.0154
Timor-Leste United Kingdom Yemen, Rep.
Predicted 0.695 1.0207 0.7265
cvpred 0.705 1.0295 0.7225
LTR 0.583 0.9900 0.6390
CV residual -0.122 -0.0395 -0.0835
Sum of squares = 0.1 Mean square = 0 n = 23
fold 2
Observations in test set: 24
Armenia Brunei Darussalam Chad Dominican Republic Ecuador
Predicted 0.9737 0.958 0.594 0.89483 0.8987
cvpred 0.9644 0.964 0.649 0.89802 0.8927
LTR 0.9960 0.952 0.345 0.89500 0.9190
CV residual 0.0316 -0.012 -0.304 -0.00302 0.0263
Egypt, Arab Rep. El Salvador Estonia Gabon Ghana Greece
Predicted 0.865 0.9125 1.00116 0.87207 0.7515 1.0101
cvpred 0.868 0.9079 1.00276 0.89368 0.7687 1.0111
LTR 0.720 0.8450 0.99800 0.88400 0.6730 0.9720
CV residual -0.148 -0.0629 -0.00476 -0.00968 -0.0957 -0.0391
Iraq Japan Mexico Moldova Mozambique Namibia Nigeria
Predicted 0.8532 0.9990 0.9056 0.844 0.6020 0.9229 0.705
cvpred 0.8663 1.0026 0.9102 0.847 0.6489 0.9416 0.744
LTR 0.7820 0.9900 0.9310 0.985 0.5610 0.8880 0.613
CV residual -0.0843 -0.0126 0.0208 0.138 -0.0879 -0.0536 -0.131
Panama Papua New Guinea Singapore Uruguay Uzbekistan Zambia
Predicted 0.982 0.669 1.0185 0.98017 0.790 0.673672
cvpred 0.963 0.709 1.0141 0.97669 0.795 0.712897
LTR 0.941 0.606 0.9590 0.98100 0.994 0.712000
CV residual -0.022 -0.103 -0.0551 0.00431 0.199 -0.000897
Sum of squares = 0.24 Mean square = 0.01 n = 24
fold 3
Observations in test set: 24
Argentina Bangladesh Botswana Brazil Costa Rica Hungary
Predicted 0.95283 0.739 0.80965 0.9375 0.8920 0.9714
cvpred 0.96849 0.732 0.85223 0.9392 0.8765 0.9767
LTR 0.97800 0.568 0.84500 0.9040 0.9620 0.9900
CV residual 0.00951 -0.164 -0.00723 -0.0352 0.0855 0.0133
Italy Malaysia Mali Montenegro Poland Portugal
Predicted 1.0478 0.91402 0.647 1.0265 0.98637 0.9946
cvpred 1.0534 0.93319 0.668 1.0474 0.98848 0.9928
LTR 0.9890 0.93100 0.311 0.9840 0.99500 0.9520
CV residual -0.0644 -0.00219 -0.357 -0.0634 0.00652 -0.0408
Russian Federation Samoa Saudi Arabia Slovenia Spain
Predicted 0.96452 0.803 1.007 0.9894 1.0417
cvpred 0.99143 0.740 1.035 0.9815 1.0289
LTR 0.99600 0.988 0.866 0.9970 0.9770
CV residual 0.00457 0.248 -0.169 0.0155 -0.0519
Sudan Sweden Switzerland Syrian Arab Republic Tanzania
Predicted 0.72881 1.021 1.030 0.8277 0.6756
cvpred 0.71989 1.016 1.027 0.8186 0.6871
LTR 0.71100 0.990 0.990 0.8340 0.7320
CV residual -0.00889 -0.026 -0.037 0.0154 0.0449
Uganda United Arab Emirates
Predicted 0.612 0.9129
cvpred 0.626 0.9566
LTR 0.732 0.9000
CV residual 0.106 -0.0566
Sum of squares = 0.28 Mean square = 0.01 n = 24
fold 4
Observations in test set: 24
Angola Bahrain Canada China Colombia Croatia Cyprus
Predicted 0.7081 0.9195 0.9666 0.835 0.9131 0.9826 0.9643
cvpred 0.6514 0.8795 0.9445 0.815 0.9007 0.9753 0.9423
LTR 0.7010 0.9190 0.9900 0.943 0.9340 0.9880 0.9830
CV residual 0.0496 0.0395 0.0455 0.128 0.0333 0.0127 0.0407
Equatorial Guinea Germany Guatemala Mongolia Netherlands
Predicted 0.772 1.0281 0.8735 0.817 1.0038
cvpred 0.701 1.0107 0.8487 0.786 0.9782
LTR 0.939 0.9900 0.7520 0.974 0.9900
CV residual 0.238 -0.0207 -0.0967 0.188 0.0118
Paraguay Qatar Romania Serbia South Africa Tajikistan
Predicted 0.8612 0.871 0.9492 0.97553 0.852 0.794
cvpred 0.8427 0.791 0.9365 0.98334 0.809 0.778
LTR 0.9390 0.963 0.9770 0.97900 0.930 0.997
CV residual 0.0963 0.172 0.0405 -0.00434 0.121 0.219
Trinidad and Tobago Turkmenistan Ukraine United States Vanuatu
Predicted 0.9322 0.793 0.9184 0.9799 0.8060
cvpred 0.8909 0.750 0.9103 0.9551 0.7761
LTR 0.9880 0.996 0.9970 0.9900 0.8260
CV residual 0.0971 0.246 0.0867 0.0349 0.0499
Vietnam
Predicted 0.8844
cvpred 0.8822
LTR 0.9320
CV residual 0.0498
Sum of squares = 0.31 Mean square = 0.01 n = 24
Overall (Sum over all 24 folds)
ms
0.00989
ms.g.step <- CVlm(df=ltrdata10, form.lm=g, m=4, seed=seed, plotit=F, printit=T)
Analysis of Variance Table
Response: LTR
Df Sum Sq Mean Sq F value Pr(>F)
GDP 1 0.932 0.932 118.89 < 2e-16
UNEMP 1 0.006 0.006 0.71 0.4002
URBGR 1 0.158 0.158 20.19 2.1e-05
MOBILE 1 0.176 0.176 22.45 8.2e-06
INTERNET 1 0.003 0.003 0.34 0.5624
LEXP 1 0.077 0.077 9.79 0.0024
Residuals 88 0.689 0.008
fold 1
Observations in test set: 23
Antigua and Barbuda Aruba Bosnia and Herzegovina
Predicted 1.00851 0.979 0.9482
cvpred 0.99366 0.989 0.9121
LTR 0.99000 0.968 0.9790
CV residual -0.00366 -0.021 0.0669
Congo, Dem. Rep. Finland France Georgia Honduras India
Predicted 0.598 1.0368 0.98271 0.9148 0.8890 0.770
cvpred 0.522 1.0352 0.98378 0.9044 0.8986 0.788
LTR 0.668 0.9990 0.99000 0.9970 0.8480 0.740
CV residual 0.146 -0.0362 0.00622 0.0926 -0.0506 -0.048
Jamaica Jordan Kazakhstan Kenya Latvia Lithuania
Predicted 0.9513 0.9158 0.916 0.789 0.971 1.0178
cvpred 0.9527 0.9129 0.932 0.728 0.952 1.0023
LTR 0.8660 0.9260 0.997 0.874 0.998 0.9970
CV residual -0.0867 0.0131 0.065 0.146 0.046 -0.0053
Macedonia, FYR Nepal Puerto Rico Sri Lanka Suriname
Predicted 0.9883 0.673 0.9922 0.8820 0.9624
cvpred 0.9429 0.688 0.9967 0.8993 0.9697
LTR 0.9730 0.603 0.9040 0.9120 0.9470
CV residual 0.0301 -0.085 -0.0927 0.0127 -0.0227
Timor-Leste United Kingdom Yemen, Rep.
Predicted 0.697 1.012 0.7263
cvpred 0.713 1.011 0.7206
LTR 0.583 0.990 0.6390
CV residual -0.130 -0.021 -0.0816
Sum of squares = 0.12 Mean square = 0.01 n = 23
fold 2
Observations in test set: 24
Armenia Brunei Darussalam Chad Dominican Republic Ecuador
Predicted 0.9782 0.9629 0.588 0.8979 0.9027
cvpred 0.9748 0.9716 0.633 0.9043 0.9001
LTR 0.9960 0.9520 0.345 0.8950 0.9190
CV residual 0.0212 -0.0196 -0.288 -0.0093 0.0189
Egypt, Arab Rep. El Salvador Estonia Gabon Ghana Greece
Predicted 0.862 0.9197 0.9902 0.8862 0.7515 1.0202
cvpred 0.864 0.9197 0.9879 0.9167 0.7667 1.0298
LTR 0.720 0.8450 0.9980 0.8840 0.6730 0.9720
CV residual -0.144 -0.0747 0.0101 -0.0327 -0.0937 -0.0578
Iraq Japan Mexico Moldova Mozambique Namibia Nigeria
Predicted 0.868 0.99525 0.91314 0.837 0.5909 0.9354 0.694
cvpred 0.891 0.99782 0.92221 0.834 0.6258 0.9702 0.725
LTR 0.782 0.99000 0.93100 0.985 0.5610 0.8880 0.613
CV residual -0.109 -0.00782 0.00879 0.151 -0.0648 -0.0822 -0.112
Panama Papua New Guinea Singapore Uruguay Uzbekistan Zambia
Predicted 0.9843 0.673 1.0177 0.98160 0.787 0.66966
cvpred 0.9699 0.708 1.0147 0.97993 0.787 0.70329
LTR 0.9410 0.606 0.9590 0.98100 0.994 0.71200
CV residual -0.0289 -0.102 -0.0557 0.00107 0.207 0.00871
Sum of squares = 0.24 Mean square = 0.01 n = 24
fold 3
Observations in test set: 24
Argentina Bangladesh Botswana Brazil Costa Rica Hungary
Predicted 0.9519 0.741 0.81443 0.9411 0.8976 0.963
cvpred 0.9674 0.733 0.85366 0.9418 0.8812 0.971
LTR 0.9780 0.568 0.84500 0.9040 0.9620 0.990
CV residual 0.0106 -0.165 -0.00866 -0.0378 0.0808 0.019
Italy Malaysia Mali Montenegro Poland Portugal
Predicted 1.0550 0.9074 0.642 1.0296 0.9801 0.9981
cvpred 1.0588 0.9277 0.663 1.0497 0.9843 0.9957
LTR 0.9890 0.9310 0.311 0.9840 0.9950 0.9520
CV residual -0.0698 0.0033 -0.352 -0.0657 0.0107 -0.0437
Russian Federation Samoa Saudi Arabia Slovenia Spain
Predicted 0.96324 0.816 1.013 0.9844 1.0433
cvpred 0.98966 0.752 1.039 0.9785 1.0313
LTR 0.99600 0.988 0.866 0.9970 0.9770
CV residual 0.00634 0.236 -0.173 0.0185 -0.0543
Sudan Sweden Switzerland Syrian Arab Republic Tanzania
Predicted 0.72559 1.01 1.0256 0.8329 0.6679
cvpred 0.71765 1.01 1.0245 0.8227 0.6807
LTR 0.71100 0.99 0.9900 0.8340 0.7320
CV residual -0.00665 -0.02 -0.0345 0.0113 0.0513
Uganda United Arab Emirates
Predicted 0.602 0.9115
cvpred 0.617 0.9537
LTR 0.732 0.9000
CV residual 0.115 -0.0537
Sum of squares = 0.28 Mean square = 0.01 n = 24
fold 4
Observations in test set: 24
Angola Bahrain Canada China Colombia Croatia Cyprus
Predicted 0.7110 0.9193 0.9616 0.836 0.915 0.9802 0.969
cvpred 0.6483 0.8798 0.9472 0.815 0.900 0.9765 0.940
LTR 0.7010 0.9190 0.9900 0.943 0.934 0.9880 0.983
CV residual 0.0527 0.0392 0.0428 0.128 0.034 0.0115 0.043
Equatorial Guinea Germany Guatemala Mongolia Netherlands
Predicted 0.786 1.0207 0.8818 0.822 0.99296
cvpred 0.692 1.0143 0.8446 0.783 0.98359
LTR 0.939 0.9900 0.7520 0.974 0.99000
CV residual 0.247 -0.0243 -0.0926 0.191 0.00641
Paraguay Qatar Romania Serbia South Africa Tajikistan
Predicted 0.8658 0.867 0.9497 0.9748 0.853 0.791
cvpred 0.8405 0.794 0.9359 0.9839 0.807 0.779
LTR 0.9390 0.963 0.9770 0.9790 0.930 0.997
CV residual 0.0985 0.169 0.0411 -0.0049 0.123 0.218
Trinidad and Tobago Turkmenistan Ukraine United States Vanuatu
Predicted 0.931 0.804 0.9201 0.9771 0.8154
cvpred 0.891 0.743 0.9091 0.9564 0.7714
LTR 0.988 0.996 0.9970 0.9900 0.8260
CV residual 0.097 0.253 0.0879 0.0336 0.0546
Vietnam
Predicted 0.8795
cvpred 0.8853
LTR 0.9320
CV residual 0.0467
Sum of squares = 0.32 Mean square = 0.01 n = 24
Overall (Sum over all 24 folds)
ms
0.0101
attr(ms.g, "ms"); attr(ms.g.step, "ms")
[1] 0.0101