Summaries and visualization of relationships

Reflection on the last lecture

Objectives

At the end of the lecture, you will know how to…

• Describe relationship of quantitative and qualitative variable.
• Create and read box plots and violin plots.
  
• Understand relationship of two quantitative variables.
• Count and interpret correlation.
• Create and understand scatterplots.
• Assess what relationship (covariation) occurs between your variables.

Relationship of quantitative and qualitative variables

Boxplot

g <- ggplot(dartpoints) +
  aes(x = Name, y = Width)

Boxplot

g <- ggplot(dartpoints) +
  aes(x = Name, y = Width)
  
g + geom_boxplot()

Boxplot

Also box and whisker plot, displays five-number summary.

Violin plot

g + geom_violin()

Violin plot

g + geom_violin() +
  geom_jitter(width = 0.05, alpha = 0.4)

Violin plot

g + geom_violin() +
  geom_boxplot(width = 0.15) +
  geom_jitter(width = 0.05, alpha = 0.2)

Relationship of two quantitative variables

Correlation

• A statistic describing a relationship between two continuous variables.

• To what degree is a variable y explained by x?

• Correlation coefficient r, from -1 to +1.

• Correlation does not imply causation!

• r = 1 – strong positive correlation

• r = 0.5 – moderately strong positive correlation

• r = 0 – variables are not correlated

• r = -0.2 – weak negative correlation

• r = -1 – strong negative correlation

Function cor()

cor(dartpoints$Length, dartpoints$Width)

[1] 0.7689932

cor(dartpoints$Length, dartpoints$Weight)

[1] 0.879953

cor(dartpoints$Width, dartpoints$Thickness)

[1] 0.5459291

Scatter plot

• Plot displying two continuous variables, x and y.
• x axis: explanatory variable, independent, predictor.
• y axis: dependent variable, response.

ggplot(dartpoints) +
  aes(x = Length, y = Weight) +
  geom_point()

Correlation examples

Correlation examples

Scatter plots

ggplot(data = dartpoints) +
  aes(x = Weight, y = Length) +
  geom_point()

Scatter plots

ggplot(data = dartpoints) +
  aes(x = Weight, y = Length, color = Name) + 
  geom_point(size = 3, alpha = 0.5)

Scatter plots

ggplot(data = dartpoints) +
  aes(x = Weight, y = Length, color = Name) + 
  geom_point(size = 3, alpha = 0.5) +
  labs(x = "Weight (g)", y = "Length (mm)", color = "Type",
       title = "Relationship of weight and length of dart points") +
  theme_light()

Scatter plots

ggplot(data = dartpoints) +
  aes(x = Weight, y = Length, size = Width, color = Name) + 
  geom_point(alpha = 0.5) +
  labs(x = "Weight (g)", y = "Length (mm)", color = "Type",
       title = "Relationship of weight and length of dart points") +
  theme_light()

Trends

ggplot(data = dartpoints) +
  aes(x = Weight, y = Length) + 
  geom_point(size = 3, alpha = 0.5) +
  geom_smooth() +
  labs(x = "Weight (g)", y = "Length (mm)", color = "Type",
       title = "Relationship of weight and length of dart points") +
  theme_light()

Trends

ggplot(data = dartpoints) +
  aes(x = Weight, y = Length) + 
  geom_point(size = 3, alpha = 0.5) +
  geom_smooth(method = "lm") +
  labs(x = "Weight (g)", y = "Length (mm)", color = "Type",
       title = "Relationship of weight and length of dart points") +
  theme_light()

Trends

ggplot(data = dartpoints) +
  aes(x = Weight, y = Length) + 
  geom_point(size = 3, alpha = 0.5) +
  geom_smooth(method = "lm", se = FALSE) +
  labs(x = "Weight (g)", y = "Length (mm)", color = "Type",
       title = "Relationship of weight and length of dart points") +
  theme_linedraw()

Small multiples

ggplot(data = dartpoints) +
  aes(x = Weight, y = Length) + 
  geom_point(size = 3, alpha = 0.5) +
  geom_smooth(method = "lm", se = FALSE) +
  labs(x = "Weight (g)", y = "Length (mm)", color = "Type",
       title = "Relationship of weight and length of dart points") +
  theme_linedraw() +
  facet_wrap(~Name)

Exercise

• Download data set with bronze age cups ( bacups.csv).
• Create a project in RStudio and load the data set.
• Explore the data set and its structure.
• What are the observations?
• What types of variables are there?
• Create a plot showing distribution of cup heights (H).
• Create a boxplot for cup heights divided by phases (Phase).
• Are there any outliers?
• Count correlation between cup height (H) and rim diameter (RD).
• Create a plot showing relationship between cup height and its rim diameter.
• Color cups from different phases (Phase) by differently.
• Describe the relationship, add a linear model to the plot.
• Label the axes sensibly.

Hints:
read.csv(),
str(),
colnames(),
summary(),
cor(),
ggplot() +
aes() +
geom_* + stat_*