Relationships Between Variables (Exam 1)

Question 1

side-by-side boxplots are good for…

Answer 1

• examining the relationship between a quantitative & categorical variable
• divide the data into groups based on the categorical variable, and create a boxplot of the quantitative variable within each group
• compare shapes, centers, spreads
• should see the exact same weights if they’re the exact same

Question 2

2-way tables are good for…

Answer 2

• examining the relationship between 2 categorical variables
• how does the distribution of the response variable (Y) change as the explanatory variable (X) is changed?
• the row/column totals & percentages give you the MARGINAL distribution (a single variable summary, looks at 1 variable by itself… doesn’t say anything about the relationship between X & Y) of the row/column variable
• CONDITIONAL distribution of Y is the distribution of Y given a particular value of X (can see how changing X influences the distribution of Y)

Question 3

scatterplots are good for…

Answer 3

• examining the relationship between 2 quantitative variables
• each point in the plot corresponds to one case in your data
• form (linear vs nonlinear, or no relationship)
• direction (negative vs positive)
• strength (the stronger the relationship, the more precisely points follow a pattern/form)
• outliers (for x, y, & the relationship)

Question 4

coefficient of correlation

Answer 4

used to measure the direction & strength of the linear relationship between 2 variables

Question 5

correlation

Answer 5

• r close to 1 indicates a strong positive linear relationship
• r close to -1 indicates a strong negative linear relationship
• r close to 0 indicates no linear relationship
• strongly affected by outliers
• symmetric (correlation between X and Y is the same as Y and X)
• has no units
• only describes the linear association