The following graphics demonstrate the ggplot2 package, which incorporates a “grammar of graphics” system. The idea is that any statistical graphic can be built from a small number of components combined in various ways.
ggplot(data = cdc,aes(gender,height)) + geom_boxplot() +
ggtitle("Men are Taller")
ggplot(data = cdc,aes(gender,weight)) + geom_boxplot() +
ggtitle("Men are Heavier")
ggplot(data = cdc,aes(gender,BMI)) +
geom_boxplot() +
ggtitle("BMI Reduces the Gender Gap")
Do a scatterplot of height and weight.
ggplot(data = cdc,(aes(x = height,y = weight))) +
geom_point()
The large number of points obscures the detail, but some upward drift to the right is apparent. It makes sense to create a linear model.
lm1 = lm(weight~height,data = cdc)
summary(lm1)##
## Call:
## lm(formula = weight ~ height, data = cdc)
##
## Residuals:
## Min 1Q Median 3Q Max
## -107.114 -22.488 -5.309 16.303 315.497
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -193.30051 3.84730 -50.24 <2e-16 ***
## height 5.40294 0.05716 94.52 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 33.32 on 19995 degrees of freedom
## Multiple R-squared: 0.3088, Adjusted R-squared: 0.3088
## F-statistic: 8935 on 1 and 19995 DF, p-value: < 2.2e-16This model has a residual standard error of 33.32. Think of this as the typical error made by the model. The estimated coefficient of height indicates that an extra inch of height adds an average 5.40 pounds.
Let’s see what adding gender to the model does.
lm2 = lm(weight~height+gender,data = cdc)
summary(lm2)##
## Call:
## lm(formula = weight ~ height + gender, data = cdc)
##
## Residuals:
## Min 1Q Median 3Q Max
## -107.34 -22.55 -5.74 15.69 323.08
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -117.81883 5.68976 -20.71 <2e-16 ***
## height 4.37206 0.08085 54.08 <2e-16 ***
## genderf -11.93441 0.66714 -17.89 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 33.05 on 19994 degrees of freedom
## Multiple R-squared: 0.3197, Adjusted R-squared: 0.3197
## F-statistic: 4699 on 2 and 19994 DF, p-value: < 2.2e-16There is a small reduction of the residual standard error. The increase in weight associated with an extra inch of height is reduced to 4.37, and we see that after accounting for height, we should reduce the predicted weight for a female by 11.93 pounds.
This section demonstrates some features added to R in the dplyr package, including piping.
cdc %>%
select(height,gender,weight) %>%
group_by(height,gender) %>%
summarize(mean_weight = mean(weight),
sd_weight = sd(weight),
n=n() )%>%
ungroup() -> c2## `summarise()` has grouped output by 'height'. You can override using the `.groups` argument.c2## # A tibble: 57 × 5
## height gender mean_weight sd_weight n
## <dbl> <fct> <dbl> <dbl> <int>
## 1 48 f 105 14.1 2
## 2 49 m 160 NA 1
## 3 50 f 112 NA 1
## 4 51 f 160 14.1 2
## 5 52 f 112. 61.5 2
## 6 53 f 145. 31.8 7
## 7 54 f 98.3 11.5 3
## 8 55 m 90 NA 1
## 9 55 f 135 39.7 3
## 10 56 f 117. 20.5 17
## # … with 47 more rowsp = ggplot(c2,aes(x=height,y=mean_weight,
color=gender,size = n))
p + geom_point()
We’ve restructured our data into a different shape. Look at it.
head(c2,10)## # A tibble: 10 × 5
## height gender mean_weight sd_weight n
## <dbl> <fct> <dbl> <dbl> <int>
## 1 48 f 105 14.1 2
## 2 49 m 160 NA 1
## 3 50 f 112 NA 1
## 4 51 f 160 14.1 2
## 5 52 f 112. 61.5 2
## 6 53 f 145. 31.8 7
## 7 54 f 98.3 11.5 3
## 8 55 m 90 NA 1
## 9 55 f 135 39.7 3
## 10 56 f 117. 20.5 17tail(c2,10)## # A tibble: 10 × 5
## height gender mean_weight sd_weight n
## <dbl> <fct> <dbl> <dbl> <int>
## 1 77 m 241. 38.5 78
## 2 77 f 174. 34.6 2
## 3 78 m 241. 49.0 40
## 4 78 f 173. 42.0 3
## 5 79 m 248. 57.3 15
## 6 80 m 222. 77.9 10
## 7 81 m 208. 69.3 3
## 8 82 m 208. 23.3 2
## 9 83 m 265 NA 1
## 10 84 m 260 NA 1c2 %>%
ggplot(aes(x = height, y = mean_weight, size = n,color=gender)) + geom_point()
Note that average BMI varies with age for both genders. It rises until about 60 and then declines. The yellow curve is a “loess” smoother, which summarizes the behavior of the points in the scatterplot.
ggplot(data=cdc,aes(x=age,y=BMI,color=BMI))+geom_point()+
geom_smooth(method = "loess",color="yellow")+
facet_wrap(~gender,nrow=2)## `geom_smooth()` using formula 'y ~ x'
As before the yellow curve is a loess smoother, which describes the overall pattern in the scatterplot. The red line separates the points which indicate a desire to gain weight (above the line) from those which indicate a desire to lose weight (below the line).
d <- ggplot(data = cdc,aes(x=BMI,y=BMIDes,color=DesActRatio))
d1 = d + geom_point(aes(alpha=.1)) +
geom_smooth(method="loess",color="yellow") +
geom_abline(slope=1,intercept=0,color="red")
d1## `geom_smooth()` using formula 'y ~ x'
d2 = d1 +
facet_wrap(~gender,nrow=2) +
ggtitle("Actual vs Desired BMI by Gender")
d2 ## `geom_smooth()` using formula 'y ~ x'
d3 = d1 +
facet_grid(gender~ageCat) +
ggtitle("Actual vs Desired BMI by Gender and Age")
d3## `geom_smooth()` using formula 'y ~ x'