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Below are three data sets. For each data set, do the following:
Identify which of the variables is most likely to be the explanatory variable, and which is most likely to be the response variable. Explain.
Identify whether each variable is categorical or quantitative, and classify the relationship as C→Q, C→C, or Q→Q, and explain how you know.
Determine what type of data display and description is appropriate for the relationship, and explain why.
Create an appropriate data display and describe the relationship using vocabulary appropriate to the type of data.
Describe any potential lurking (confounding) variables and describe how this impacts association (correlation) versus causation. Describe what other information you can get from this data, or what other questions you might have about it.
Here are the data sets:
A study comparing children’s height to their reading level showed that 70% of children who were less than 48 inches tall had a reading level at or below 4th grade, while 80% of children who were 48 inches or taller had a reading level above 4th grade. There are 200 students total, and 110 of them are less than 48 inches tall.
The following shows, for a small-town high school, the average salaries after graduation of the Class of 1950 (11 students) and the Class of 2000 (16 students).
1950 $2500 $2700 $4000 $3600 $2200 $2300 $2900 $3300 $3400 $2900 $3100
2000 $22000 $19000 $37000 $38000 $29000 $67000 $46000 $17000 $28000 $31000 $33000 $29000 $34000 $41000 $22000 $23000
The following chart shows the current dosage of antidepressant medication in milligrams taken by 16 people to treat their depression, followed by the number of psychiatric hospitalizations each has had to treat their depression.
Dosage (mg) # Hospitalizations
2 4
4 6
5 9
3 8
3 5
5 11
5 14
4 12
2 6
3 11
1 7
1 4
0 5
0 3
0 8
1 2

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