Chapter 12, Problem 71H

State #	letters in name	Year entered the Union	Rank for entering the Union	Area (squaremiles)
Alabama	7	1819	22	52,423
Colorado	8	1876	38	104,100
Hawaii	6	1959	50	10,932
Iowa	4	1846	29	56,276
Maryland	8	1788	7	12,407
Missouri	8	1821	24	69,709
New Jersey	9	1787	3	8,722
Ohio	4	1803	17	44,828
South Carolina	13	1788	8	32,008
Utah	4	1896	45	84,904
Wisconsin	9	1848	30	65,499

Table 12.23

We are interested in whether or not the number of letters in a state name depends upon the year the state entered the Union.

a. Decide which variable should be the independent variable and which should be the dependent variable.

b. Draw 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 number of letters (to the nearest integer) a state would have if it entered the Union in 1900.

Find the estimated number of letters a state would have if it entered the Union in 1940.

g. Does it appear that a line is the best way to fit the data? Why or why not?

h. Use the least-squares line to estimate the number of letters a new state that enters the Union this year would have.

Can the least squares line be used to predict it? Why or why not?