Final answer:
The task involves identifying independent and dependent variables in different studies and analyzing the relationship between them using statistical tools such as scatter plots, least-squares regression lines, and correlation coefficients. This helps in understanding how changes in one variable may affect another.
Step-by-step explanation:
The exercise pertains to identifying independent and dependent variables in various scenarios and understanding their roles in a statistical study. Independent variables are those that are believed to influence or cause changes in another variable, and dependent variables are those that are thought to be affected by the manipulation of the independent variable.
For instance, in scenario (55a), age is the independent variable while fatalities are the dependent variable, suggesting that the study is interested in how the age of drivers might affect the number of fatalities. In scenarios involving drawing a scatter plot and calculating the least-squares regression line (such as 80a), the relationship between the two variables is further investigated to understand correlation and prediction capabilities.
Further, calculating the correlation coefficient provides insight into the strength and direction of the relationship between the variables. When estimating values using the least-squares regression line, such as estimating the areas for Alabama and Colorado or the number of letters in a state's name based on the year it entered the Union, the significance of the predictive power of the model is scrutinized.