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(ggvis)
## Loading required package: ggvis
require(magrittr)
## Loading required package: magrittr
require(Ecdat)
## Loading required package: Ecdat
## Loading required package: Ecfun
## 
## Attaching package: 'Ecdat'
## 
## The following object is masked from 'package:datasets':
## 
##     Orange
require(corrplot)
## Loading required package: corrplot
data2<-read.csv(url("http://www.personal.psu.edu/dlp/w540/StateIndicator.csv"))
data2<-tbl_df(data2)
data2
## Source: local data frame [50 x 7]
## 
##     stateNames Population Income Illiteracy LifeExp Murder HSGrad
## 1      Alabama       3615   3624        2.1   69.05   15.1   41.3
## 2       Alaska        365   6315        1.5   69.31   11.3   66.7
## 3      Arizona       2212   4530        1.8   70.55    7.8   58.1
## 4     Arkansas       2110   3378        1.9   70.66   10.1   39.9
## 5   California      21198   5114        1.1   71.71   10.3   62.6
## 6     Colorado       2541   4884        0.7   72.06    6.8   63.9
## 7  Connecticut       3100   5348        1.1   72.48    3.1   56.0
## 8     Delaware        579   4809        0.9   70.06    6.2   54.6
## 9      Florida       8277   4815        1.3   70.66   10.7   52.6
## 10     Georgia       4931   4091        2.0   68.54   13.9   40.6
## ..         ...        ...    ...        ...     ...    ...    ...
  1. Compute and report correlations among these six variables and plot a correlogram representing these correlations.
source("http://www.sthda.com/upload/rquery_cormat.r")
state <- data2 %>% select(Population, Income, Illiteracy, LifeExp, Murder, HSGrad)
rquery.cormat(state) 

## $r
##            LifeExp Income HSGrad Population Illiteracy Murder
## LifeExp          1                                           
## Income        0.34      1                                    
## HSGrad        0.58   0.62      1                             
## Population  -0.068   0.21 -0.098          1                  
## Illiteracy   -0.59  -0.44  -0.66       0.11          1       
## Murder       -0.78  -0.23  -0.49       0.34        0.7      1
## 
## $p
##            LifeExp  Income  HSGrad Population Illiteracy Murder
## LifeExp          0                                             
## Income       0.016       0                                     
## HSGrad     9.2e-06 1.6e-06       0                             
## Population    0.64    0.15     0.5          0                  
## Illiteracy   7e-06  0.0015 2.2e-07       0.46          0       
## Murder     2.3e-11    0.11 0.00032      0.015    1.3e-08      0
## 
## $sym
##            LifeExp Income HSGrad Population Illiteracy Murder
## LifeExp    1                                                 
## Income     .       1                                         
## HSGrad     .       ,      1                                  
## Population                       1                           
## Illiteracy .       .      ,                 1                
## Murder     ,              .      .          ,          1     
## attr(,"legend")
## [1] 0 ' ' 0.3 '.' 0.6 ',' 0.8 '+' 0.9 '*' 0.95 'B' 1
  1. Using ggvis, construct

  1. plots that demonstrate the relationship between

  2. HSGrad and Income, and

state %>% ggvis(~HSGrad, ~Income) %>% layer_points() %>% layer_smooths()

  1. Illiteracy and Income.
state %>% ggvis(~Illiteracy, ~Income) %>% layer_points() %>% layer_smooths()

  1. A scatterplot of Murder by Illiteracy grouped by HSGrad.
state %>% ggvis(~Illiteracy, ~Murder) %>% layer_points(fill = ~factor(HSGrad))

  1. Report tests of null hypotheses that
  1. there is no difference in Income between states above median HSGrad and states less than or equal to median HSGrad, and
state$median<-ifelse(state$Income>median(state$Income),1,0)
t.test(state$Income~state$median)
## 
##  Welch Two Sample t-test
## 
## data:  state$Income by state$median
## t = -9.0052, df = 47.995, p-value = 6.973e-12
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -1179.5304  -748.9496
## sample estimates:
## mean in group 0 mean in group 1 
##         3953.68         4917.92

According to the result of t-test, the null hypothesis is rejected. In other words, there is difference in income between states above median HSGrad and states less than or equal to median HSGrad.

  1. there is no difference in Murder between one group of states (to include Alabama, Alaska, Arkansas, Georgia, Illinois, Kentucky, Louisiana, Mississippi, and Michigan) and another group of states (Arizona, Connecticut, Iowa, Kansas, Maine, Minnesota, Nebraska, New Hampshire, North Dakota).
require(car)
## Loading required package: car
## 
## Attaching package: 'car'
## 
## The following object is masked from 'package:Ecdat':
## 
##     Mroz
state$state<- recode(data2$stateNames, '"Alabama" = 1; "Alaska" =1; "Arkansas"=1; "Georgia"=1; "Illinois"=1; "Kentucky"=1; "Louisiana"=1; "Mississippi"=1; "Michigan"=1; else=0')
t.test(state$Murder~state$state)
## 
##  Welch Two Sample t-test
## 
## data:  state$Murder by state$state
## t = -7.3491, df = 21.544, p-value = 2.667e-07
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -7.246531 -4.053740
## sample estimates:
## mean in group 0 mean in group 1 
##        6.360976       12.011111

According to the result of t-test, the null hypothesis is rejected. That is, there is statistically significant difference between two groups.