We are interested in whether there is a relationship between the ranking of a state and the area of the state.
a. Let rank be the independent variable and area be the dependent variable.
b. What do you think the scatter plot will look like? Make a scatter plot of the data.
c. Does it appear from inspection that there is a relationship between the variables? Why or why not?
d. Calculate the least squares line. Put the equation in the form of: ^ y= a + bx
e. Find the correlation coefficient. What does it imply about the significance of the relationship?
f. Find the estimated areas for Alabama and for Colorado. Are they close to the actual areas?
g. Use the two points in (f) to plot the least squares line on your graph from (b).
h. Does it appear that a line is the best way to fit the data? Why or why not?
i. Are there any outliers?
j. Use the least squares line to estimate the area of a new state that enters the Union. Can the least squares line be used to predict it? Why or why not?
k. Delete "Hawaii" and substitute "Alaska" for it. Alaska is the fortieth state with an area of 656,424 square miles.
l. Calculate the new least squares line.
m. Find the estimated area for Alabama. Is it closer to the actual area with this new least squares line or with the previous one that included Hawaii? Why do you think that's the case?
n. Do you think that, in general, newer states are larger than the original states?