First I installed the necessary packages.

I selected four continuous variables from Mroz. The variables are agew, educw, hoursw, and wagew.

contvar <- Mroz %>%
  select(hoursw, agew, educw, wagew)
tbl_df (contvar)
## Source: local data frame [753 x 4]
## 
##    hoursw agew educw wagew
## 1    1610   32    12  2.65
## 2    1656   30    12  2.65
## 3    1980   35    12  4.04
## 4     456   34    12  3.25
## 5    1568   31    14  3.60
## 6    2032   54    12  4.70
## 7    1440   37    16  5.95
## 8    1020   54    12  9.98
## 9    1458   48    12  0.00
## 10   1600   39    12  4.15
## ..    ...  ...   ...   ...

Then I estimated Pearson Product-Moment Correlations for four pairs of variables. I loaded the cormat functions.

## $r
##          agew educw hoursw wagew
## agew        1                   
## educw   -0.12     1             
## hoursw -0.033  0.11      1      
## wagew  -0.058  0.27   0.61     1
## 
## $p
##           agew   educw hoursw wagew
## agew         0                     
## educw  0.00095       0             
## hoursw    0.36  0.0036      0      
## wagew     0.11 8.2e-14      0     0
## 
## $sym
##        agew educw hoursw wagew
## agew   1                      
## educw       1                 
## hoursw            1           
## wagew             ,      1    
## attr(,"legend")
## [1] 0 ' ' 0.3 '.' 0.6 ',' 0.8 '+' 0.9 '*' 0.95 'B' 1

Next, I tested the null hypotheses that the population correlations = 0 for the four pairs of variables I selected.

The null hypothesis is that there is no correlation between agew, educw, hoursw, and wagew. The alpha is equal to 0.05. I would reject the null hypothesis that there is no correlation between educw and hoursw as well as educw and wagew because the p-value is less than 0.05. However, I would fail to reject the null hypothesis that there is no correlation between hourw and agew, agew and wagew because the p-value is greater than alpha.

Then, I Used ggvis to plot scatterplots containing points and a smooth line for the four pairs of variable I selected.

ggvis(Mroz, x = ~hoursw, y = ~agew) %>% layer_points()%>% layer_smooths()

ggvis(Mroz, x = ~hoursw, y = ~wagew) %>% layer_points()%>% layer_smooths()

ggvis(Mroz, x = ~hoursw, y = ~educw) %>% layer_points()%>% layer_smooths()

ggvis(Mroz, x = ~wagew, y = ~educw) %>% layer_points()%>% layer_smooths()

Finally, I produced correlograms and heat maps for the four pairs of variables I selected.

## Source: local data frame [753 x 2]
## 
##    hoursw agew
## 1    1610   32
## 2    1656   30
## 3    1980   35
## 4     456   34
## 5    1568   31
## 6    2032   54
## 7    1440   37
## 8    1020   54
## 9    1458   48
## 10   1600   39
## ..    ...  ...

## $r
##        hoursw agew
## hoursw      1     
## agew   -0.033    1
## 
## $p
##        hoursw agew
## hoursw      0     
## agew     0.36    0
## 
## $sym
##        hoursw agew
## hoursw 1          
## agew          1   
## attr(,"legend")
## [1] 0 ' ' 0.3 '.' 0.6 ',' 0.8 '+' 0.9 '*' 0.95 'B' 1

## Source: local data frame [753 x 2]
## 
##    hoursw wagew
## 1    1610  2.65
## 2    1656  2.65
## 3    1980  4.04
## 4     456  3.25
## 5    1568  3.60
## 6    2032  4.70
## 7    1440  5.95
## 8    1020  9.98
## 9    1458  0.00
## 10   1600  4.15
## ..    ...   ...

## $r
##        hoursw wagew
## hoursw      1      
## wagew    0.61     1
## 
## $p
##        hoursw wagew
## hoursw      0      
## wagew       0     0
## 
## $sym
##        hoursw wagew
## hoursw 1           
## wagew  ,      1    
## attr(,"legend")
## [1] 0 ' ' 0.3 '.' 0.6 ',' 0.8 '+' 0.9 '*' 0.95 'B' 1

## Source: local data frame [753 x 2]
## 
##    hoursw educw
## 1    1610    12
## 2    1656    12
## 3    1980    12
## 4     456    12
## 5    1568    14
## 6    2032    12
## 7    1440    16
## 8    1020    12
## 9    1458    12
## 10   1600    12
## ..    ...   ...

## $r
##        hoursw educw
## hoursw      1      
## educw    0.11     1
## 
## $p
##        hoursw educw
## hoursw      0      
## educw  0.0036     0
## 
## $sym
##        hoursw educw
## hoursw 1           
## educw         1    
## attr(,"legend")
## [1] 0 ' ' 0.3 '.' 0.6 ',' 0.8 '+' 0.9 '*' 0.95 'B' 1

## Source: local data frame [753 x 2]
## 
##    wagew educw
## 1   2.65    12
## 2   2.65    12
## 3   4.04    12
## 4   3.25    12
## 5   3.60    14
## 6   4.70    12
## 7   5.95    16
## 8   9.98    12
## 9   0.00    12
## 10  4.15    12
## ..   ...   ...

## $r
##       wagew educw
## wagew     1      
## educw  0.27     1
## 
## $p
##         wagew educw
## wagew       0      
## educw 8.2e-14     0
## 
## $sym
##       wagew educw
## wagew 1          
## educw       1    
## attr(,"legend")
## [1] 0 ' ' 0.3 '.' 0.6 ',' 0.8 '+' 0.9 '*' 0.95 'B' 1