Final Exam Task2
Woongbae Park
November 28, 2015
## Source: local data frame [50 x 7]
##
## stateNames Population Income Illiteracy LifeExp Murder HSGrad
## (fctr) (int) (int) (dbl) (dbl) (dbl) (dbl)
## 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
## .. ... ... ... ... ... ... ...## stateNames Population Income Illiteracy
## Alabama : 1 Min. : 365 Min. :3098 Min. :0.500
## Alaska : 1 1st Qu.: 1080 1st Qu.:3993 1st Qu.:0.625
## Arizona : 1 Median : 2838 Median :4519 Median :0.950
## Arkansas : 1 Mean : 4246 Mean :4436 Mean :1.170
## California: 1 3rd Qu.: 4968 3rd Qu.:4814 3rd Qu.:1.575
## Colorado : 1 Max. :21198 Max. :6315 Max. :2.800
## (Other) :44
## LifeExp Murder HSGrad
## Min. :67.96 Min. : 1.400 Min. :37.80
## 1st Qu.:70.12 1st Qu.: 4.350 1st Qu.:48.05
## Median :70.67 Median : 6.850 Median :53.25
## Mean :70.88 Mean : 7.378 Mean :53.11
## 3rd Qu.:71.89 3rd Qu.:10.675 3rd Qu.:59.15
## Max. :73.60 Max. :15.100 Max. :67.30
## ## Classes 'tbl_df', 'tbl' and 'data.frame': 50 obs. of 7 variables:
## $ stateNames: Factor w/ 50 levels "Alabama","Alaska",..: 1 2 3 4 5 6 7 8 9 10 ...
## $ Population: int 3615 365 2212 2110 21198 2541 3100 579 8277 4931 ...
## $ Income : int 3624 6315 4530 3378 5114 4884 5348 4809 4815 4091 ...
## $ Illiteracy: num 2.1 1.5 1.8 1.9 1.1 0.7 1.1 0.9 1.3 2 ...
## $ LifeExp : num 69 69.3 70.5 70.7 71.7 ...
## $ Murder : num 15.1 11.3 7.8 10.1 10.3 6.8 3.1 6.2 10.7 13.9 ...
## $ HSGrad : num 41.3 66.7 58.1 39.9 62.6 63.9 56 54.6 52.6 40.6 ...## Source: local data frame [6 x 7]
##
## stateNames Population Income Illiteracy LifeExp Murder HSGrad
## (fctr) (int) (int) (dbl) (dbl) (dbl) (dbl)
## 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 63.9Use Stateindic built-in dataset and retain in States only the continuous variables from Stateindic.
States <- Stateindic %>%
select(Population, Income, Illiteracy, LifeExp, Murder, HSGrad)
States## Source: local data frame [50 x 6]
##
## Population Income Illiteracy LifeExp Murder HSGrad
## (int) (int) (dbl) (dbl) (dbl) (dbl)
## 1 3615 3624 2.1 69.05 15.1 41.3
## 2 365 6315 1.5 69.31 11.3 66.7
## 3 2212 4530 1.8 70.55 7.8 58.1
## 4 2110 3378 1.9 70.66 10.1 39.9
## 5 21198 5114 1.1 71.71 10.3 62.6
## 6 2541 4884 0.7 72.06 6.8 63.9
## 7 3100 5348 1.1 72.48 3.1 56.0
## 8 579 4809 0.9 70.06 6.2 54.6
## 9 8277 4815 1.3 70.66 10.7 52.6
## 10 4931 4091 2.0 68.54 13.9 40.6
## .. ... ... ... ... ... ...Load the cormat functions.
source("http://www.sthda.com/upload/rquery_cormat.r")1. Compute and report correlations among these six variables and plot a correlogram representing these correlations.
rquery.cormat(States)
## $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
##
## $sym
## LifeExp Income HSGrad Population Illiteracy Murder
## LifeExp 1
## Income . 1
## HSGrad . , 1
## Population 1
## Illiteracy . . , 1
## Murder , . . , 1
## attr(,"legend")
## [1] 0 ' ' 0.3 '.' 0.6 ',' 0.8 '+' 0.9 '*' 0.95 'B' 12. Using ggvis, construct
####a. plots that demonstrate the relationship between ####i. HSGrad and Income
States %>% ggvis(x=~HSGrad, y=~Income) %>% layer_points() %>% layer_smooths()States %>% ggvis(x=~Illiteracy, y=~Income) %>% layer_points() %>% layer_smooths()####b. A scatterplot of Murder by Illiteracy grouped by HSGrad
States %>% ggvis(x=~Illiteracy, y= ~Murder) %>% layer_points(fill= ~factor(HSGrad)) %>% group_by(HSGrad) 3. Report tests of null hypotheses that
a. there is no difference in Income between states above median HSGrad and states less than or equal to median HSGrad, and
median(States$HSGrad)## [1] 53.25aboveHSGrad<-filter(Stateindic, HSGrad > 53.25)
aboveHSGrad## Source: local data frame [25 x 7]
##
## stateNames Population Income Illiteracy LifeExp Murder HSGrad
## (fctr) (int) (int) (dbl) (dbl) (dbl) (dbl)
## 1 Alaska 365 6315 1.5 69.31 11.3 66.7
## 2 Arizona 2212 4530 1.8 70.55 7.8 58.1
## 3 California 21198 5114 1.1 71.71 10.3 62.6
## 4 Colorado 2541 4884 0.7 72.06 6.8 63.9
## 5 Connecticut 3100 5348 1.1 72.48 3.1 56.0
## 6 Delaware 579 4809 0.9 70.06 6.2 54.6
## 7 Hawaii 868 4963 1.9 73.60 6.2 61.9
## 8 Idaho 813 4119 0.6 71.87 5.3 59.5
## 9 Iowa 2861 4628 0.5 72.56 2.3 59.0
## 10 Kansas 2280 4669 0.6 72.58 4.5 59.9
## .. ... ... ... ... ... ... ...I.aboveHSGrad <-aboveHSGrad$Income
lessHSGrad <- filter (Stateindic, HSGrad <= 53.25)
lessHSGrad## Source: local data frame [25 x 7]
##
## stateNames Population Income Illiteracy LifeExp Murder HSGrad
## (fctr) (int) (int) (dbl) (dbl) (dbl) (dbl)
## 1 Alabama 3615 3624 2.1 69.05 15.1 41.3
## 2 Arkansas 2110 3378 1.9 70.66 10.1 39.9
## 3 Florida 8277 4815 1.3 70.66 10.7 52.6
## 4 Georgia 4931 4091 2.0 68.54 13.9 40.6
## 5 Illinois 11197 5107 0.9 70.14 10.3 52.6
## 6 Indiana 5313 4458 0.7 70.88 7.1 52.9
## 7 Kentucky 3387 3712 1.6 70.10 10.6 38.5
## 8 Louisiana 3806 3545 2.8 68.76 13.2 42.2
## 9 Maryland 4122 5299 0.9 70.22 8.5 52.3
## 10 Michigan 9111 4751 0.9 70.63 11.1 52.8
## .. ... ... ... ... ... ... ...I.lesseHSGrad<- lessHSGrad$Income
t.test(I.aboveHSGrad, I.lesseHSGrad, var.eq=TRUE)##
## Two Sample t-test
##
## data: I.aboveHSGrad and I.lesseHSGrad
## t = 1.9642, df = 48, p-value = 0.05531
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -7.838476 671.518476
## sample estimates:
## mean of x mean of y
## 4601.72 4269.88The p-value associated with a t-value of 1.9642 equals 0.05531 which is >α. Therefore, null cannot be rejected at α = .05. We fail to reject the null hypothesis that there is no difference in Income between states above median HSGrad and states less than or equal to median HSGrad.
b. 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).
Group1 <- c("Alabama", "Alaska", "Arkansas", "Georgia", "Illinois", "Kentucky", "Louisiana","Mississippi", "Michigan")
Group1f<-filter (Stateindic, stateNames %in% Group1)
Group1f## Source: local data frame [9 x 7]
##
## stateNames Population Income Illiteracy LifeExp Murder HSGrad
## (fctr) (int) (int) (dbl) (dbl) (dbl) (dbl)
## 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 Arkansas 2110 3378 1.9 70.66 10.1 39.9
## 4 Georgia 4931 4091 2.0 68.54 13.9 40.6
## 5 Illinois 11197 5107 0.9 70.14 10.3 52.6
## 6 Kentucky 3387 3712 1.6 70.10 10.6 38.5
## 7 Louisiana 3806 3545 2.8 68.76 13.2 42.2
## 8 Michigan 9111 4751 0.9 70.63 11.1 52.8
## 9 Mississippi 2341 3098 2.4 68.09 12.5 41.0Group2 <- c ("Arizona", "Connecticut", "Iowa", "Kansas", "Maine", "Minnesota", "Nebraska", "New Hampshire", "North Dakota")
Group2f<-filter (Stateindic, stateNames %in% Group2)
Group2f## Source: local data frame [9 x 7]
##
## stateNames Population Income Illiteracy LifeExp Murder HSGrad
## (fctr) (int) (int) (dbl) (dbl) (dbl) (dbl)
## 1 Arizona 2212 4530 1.8 70.55 7.8 58.1
## 2 Connecticut 3100 5348 1.1 72.48 3.1 56.0
## 3 Iowa 2861 4628 0.5 72.56 2.3 59.0
## 4 Kansas 2280 4669 0.6 72.58 4.5 59.9
## 5 Maine 1058 3694 0.7 70.39 2.7 54.7
## 6 Minnesota 3921 4675 0.6 72.96 2.3 57.6
## 7 Nebraska 1544 4508 0.6 72.60 2.9 59.3
## 8 New Hampshire 812 4281 0.7 71.23 3.3 57.6
## 9 North Dakota 637 5087 0.8 72.78 1.4 50.3m.Group1 <-Group1f$Murder
m.Group1## [1] 15.1 11.3 10.1 13.9 10.3 10.6 13.2 11.1 12.5m.Group2 <-Group2f$Murder
m.Group2## [1] 7.8 3.1 2.3 4.5 2.7 2.3 2.9 3.3 1.4t.test(m.Group1, m.Group2, var.eq=TRUE)##
## Two Sample t-test
##
## data: m.Group1 and m.Group2
## t = 10.124, df = 16, p-value = 2.312e-08
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 6.834422 10.454467
## sample estimates:
## mean of x mean of y
## 12.011111 3.366667