Final answer:
The data required to determine the relationship between age and the ability to name U.S. states in 60 seconds is not provided. Instead, discussions of correlations such as the number of letters in a state name and its year of statehood, age and driver fatality rates, and year and flu cases are given, demonstrating how positive, negative, and zero correlations are interpreted and calculated.
Step-by-step explanation:
The relationship between age and the number of U.S. states a person can name in 60 seconds is not provided in the data. Instead, different correlational relationships are discussed, such as between the number of letters in a state name and the year the state entered the Union, driver fatalities and age, and the number of diagnosed flu cases over time.
Correlation measures the strength and direction of a linear relationship between two variables. It can be positive, negative, or zero (no correlation). Positive correlation implies that as one variable increases, so does the other, while negative correlation indicates that as one variable increases, the other decreases. Zero correlation means there is no discernible linear relationship between the variables.
For example, in the context of driver fatalities as a function of driver age, age would be the independent variable, and the number of driver deaths per 100,000 people would be the dependent variable. A scatter plot could be made from this data to visualize the relationship, followed by the calculation of the least-squares (best-fit) line and the correlation coefficient to interpret the data's significance and predict outcomes. The slope of the least-squares line would provide the rate of change of the dependent variable for each unit change in the independent variable.