Final answer:
The independent variable is the ranking of a state, while the dependent variable is the area of the state. A scatter plot would show a positive relationship between the ranking of a state and its area. From inspection, it appears that there is a relationship between the variables. The least-squares line can be found using linear regression, and the correlation coefficient can determine the strength and direction of the relationship.
Step-by-step explanation:
a. Independent and Dependent Variables:
The independent variable is the ranking of a state, while the dependent variable is the area of the state.
b. Scatter Plot:
Based on the given data, we can expect the scatter plot to show a positive relationship between the ranking of a state and its area.
c. Relationship Between Variables:
From inspection, it appears that there is a relationship between the variables. As the ranking of a state increases, the area of the state also tends to increase.
d. Least-Squares Line:
To find the least-squares line, we can use linear regression. The equation of the least-squares line is ŷ = a + bx, where ŷ represents the predicted area, a represents the y-intercept, b represents the slope, and x represents the ranking of a state.
e. Correlation Coefficient:
We can find the correlation coefficient, which measures the strength and direction of the relationship. If the correlation coefficient is close to 1, it implies a strong positive relationship between the variables. If it is close to -1, it implies a strong negative relationship. If it is close to 0, it implies little to no relationship.
f. Estimated Areas:
Using the least-squares line, we can estimate the areas for specific rankings. For example, we can find the estimated area for Alabama and Colorado by plugging in their respective rankings in the equation.