Assignment #4
Woongbae Park
November 19, 2015
require(corrplot)
## Loading required package: corrplot
require(dplyr)
## Loading required package: dplyr
##
## Attaching package: 'dplyr'
##
## The following objects are masked from 'package:stats':
##
## filter, lag
##
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
require(Ecdat)
## Loading required package: Ecdat
## Loading required package: Ecfun
##
## Attaching package: 'Ecdat'
##
## The following object is masked from 'package:datasets':
##
## Orange
require(ggvis)
## Loading required package: ggvis
data(Mroz)
names(Mroz)
## [1] "work" "hoursw" "child6" "child618" "agew"
## [6] "educw" "hearnw" "wagew" "hoursh" "ageh"
## [11] "educh" "wageh" "income" "educwm" "educwf"
## [16] "unemprate" "city" "experience"
summary(Mroz)
## work hoursw child6 child618
## yes:325 Min. : 0.0 Min. :0.0000 Min. :0.000
## no :428 1st Qu.: 0.0 1st Qu.:0.0000 1st Qu.:0.000
## Median : 288.0 Median :0.0000 Median :1.000
## Mean : 740.6 Mean :0.2377 Mean :1.353
## 3rd Qu.:1516.0 3rd Qu.:0.0000 3rd Qu.:2.000
## Max. :4950.0 Max. :3.0000 Max. :8.000
## agew educw hearnw wagew
## Min. :30.00 Min. : 5.00 Min. : 0.000 Min. :0.00
## 1st Qu.:36.00 1st Qu.:12.00 1st Qu.: 0.000 1st Qu.:0.00
## Median :43.00 Median :12.00 Median : 1.625 Median :0.00
## Mean :42.54 Mean :12.29 Mean : 2.375 Mean :1.85
## 3rd Qu.:49.00 3rd Qu.:13.00 3rd Qu.: 3.788 3rd Qu.:3.58
## Max. :60.00 Max. :17.00 Max. :25.000 Max. :9.98
## hoursh ageh educh wageh
## Min. : 175 Min. :30.00 Min. : 3.00 Min. : 0.4121
## 1st Qu.:1928 1st Qu.:38.00 1st Qu.:11.00 1st Qu.: 4.7883
## Median :2164 Median :46.00 Median :12.00 Median : 6.9758
## Mean :2267 Mean :45.12 Mean :12.49 Mean : 7.4822
## 3rd Qu.:2553 3rd Qu.:52.00 3rd Qu.:15.00 3rd Qu.: 9.1667
## Max. :5010 Max. :60.00 Max. :17.00 Max. :40.5090
## income educwm educwf unemprate
## Min. : 1500 Min. : 0.000 Min. : 0.000 Min. : 3.000
## 1st Qu.:15428 1st Qu.: 7.000 1st Qu.: 7.000 1st Qu.: 7.500
## Median :20880 Median :10.000 Median : 7.000 Median : 7.500
## Mean :23081 Mean : 9.251 Mean : 8.809 Mean : 8.624
## 3rd Qu.:28200 3rd Qu.:12.000 3rd Qu.:12.000 3rd Qu.:11.000
## Max. :96000 Max. :17.000 Max. :17.000 Max. :14.000
## city experience
## no :269 Min. : 0.00
## yes:484 1st Qu.: 4.00
## Median : 9.00
## Mean :10.63
## 3rd Qu.:15.00
## Max. :45.00
1. Select several continuous variables from Mroz.
Mroz1 <- Mroz %>%
select(wagew, income, agew, ageh)
head(Mroz1)
## wagew income agew ageh
## 1 2.65 16310 32 34
## 2 2.65 21800 30 30
## 3 4.04 21040 35 40
## 4 3.25 7300 34 53
## 5 3.60 27300 31 32
## 6 4.70 19495 54 57
2. Estimate Pearson Product-Moment Correlations for four pairs of variables.
rquery.cormat(Mroz1)
## $r
## agew ageh wagew income
## agew 1
## ageh 0.89 1
## wagew -0.058 -0.055 1
## income 0.052 0.041 0.21 1
##
## $p
## agew ageh wagew income
## agew 0
## ageh 0 0
## wagew 0.11 0.13 0
## income 0.15 0.27 7.4e-09 0
##
## $sym
## agew ageh wagew income
## agew 1
## ageh + 1
## wagew 1
## income 1
## attr(,"legend")
## [1] 0 ' ' 0.3 '.' 0.6 ',' 0.8 '+' 0.9 '*' 0.95 'B' 1
3. Test null hypotheses that the population correlations = 0 for the four pairs of variables you selected.
cor.test(Mroz1$income, Mroz1$wagew)
##
## Pearson's product-moment correlation
##
## data: Mroz1$income and Mroz1$wagew
## t = 5.8484, df = 751, p-value = 7.404e-09
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.1393437 0.2760413
## sample estimates:
## cor
## 0.2087117
##### The correlation cofficient is 0.21. There is weak (small) significant positive linear correlation between income and wagew. We reject the null hypothesis.
cor.test(Mroz1$income, Mroz1$ageh)
##
## Pearson's product-moment correlation
##
## data: Mroz1$income and Mroz1$ageh
## t = 1.1109, df = 751, p-value = 0.267
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.03103299 0.11162545
## sample estimates:
## cor
## 0.04050263
The correlation cofficient is 0.04. There is no significant linear correlation between income and ageh. We fail to reject the null hypothesis.
cor.test(Mroz1$income, Mroz1$agew)
##
## Pearson's product-moment correlation
##
## data: Mroz1$income and Mroz1$agew
## t = 1.4391, df = 751, p-value = 0.1505
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.01907725 0.12342346
## sample estimates:
## cor
## 0.05244006
The correlation cofficient is 0.05. There is no significant linear correlation between income and agew. We fail to reject the null hypothesis.
cor.test(Mroz1$ageh, Mroz1$agew)
##
## Pearson's product-moment correlation
##
## data: Mroz1$ageh and Mroz1$agew
## t = 52.959, df = 751, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.8720254 0.9023277
## sample estimates:
## cor
## 0.888138
The correlation cofficient is 0.87. There is strong (large) significant positive linear correlation between ageh and agew. We reject the null hypothesis.
4. Using ggvis, plot scatterplots containing points and a smooth line for the four pairs of variable you selected.
Mroz1 %>% ggvis(x=~income, y=~wagew) %>% layer_points %>% layer_smooths()
Mroz1 %>% ggvis(x=~income, y=~agew) %>% layer_points %>% layer_smooths()
Mroz1 %>% ggvis(x=~income, y=~ageh) %>% layer_points %>% layer_smooths()
Mroz1 %>% ggvis(x=~agew, y=~ageh) %>% layer_points %>% layer_smooths()
5. Produce correlograms and heat maps for the four pairs of variables you selected.
require(corrgram)
## Loading required package: corrgram
corrgram(Mroz1, upper.panel=NULL)
cormat<-rquery.cormat(Mroz1, graphType="heatmap")
