Chapter 12, Problem 85BITH

State	# letters in name	Year entered the Union	Ranks for entering the Union	Area (squaremiles)
Alabama	7	1,819	22	52,423
Colorado	8	1,876	38	104,100
Hawaii	6	1,959	50	10,932
Iowa	4	1,846	29	56,276
Maryland	8	1,788	7	12,407
Missouri	8	1,821	24	69,709
New Jersey	9	1,787	3	8,722
Ohio	4	1,803	17	44,828
South Carolina	13	1788	8	32,008
Utah	4	1896	45	84,904
Wisconsin	9	1848	30	65,499

We are interested in whether there is a relationship between the ranking of a state and the area of the state.

a. What are the independent and dependent variables?

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: $\hat{y}\text{=}a+bx$

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 part f to plot the least-squares line on your graph from part 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 forty-ninth, 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?