| State | No. of Letters in Name | Year Entered the Union | Rank for Entering the Union | Area in square miles |
| 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 |
We are interested in whether the number of letters in a state name depends on the year the state entered the Union.
- Decide which variable should be the independent variable and which should be the dependent variable.
- Draw a scatter plot of the data.
- Does it appear from inspection that there is a relationship between the variables? Why or why not?
- Calculate the least-squares line. Put the equation in the form ŷ = a + bx.
- Find the correlation coefficient. What does it imply about the significance of the relationship?
- Find the estimated number of letters (to the nearest integer) a state name would have if it entered the Union in 1900. Find the estimated number of letters a state name would have if it entered the Union in 1940.
- Does it appear that a line is the best way to fit the data? Why or why not?
- Use the least-squares line to estimate the number of letters for a new state that enters the Union this year. Can the least-squares line be used to predict it? Why or why not?
OpenStax Statistics, 12.4 Prediction (Optional), exercise 27