| State | # letters in name | Year entered the Union | Rank for entering the Union | Area (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 or not the number of letters in a state name depends upon 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 of: 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 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.
- 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 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?
OpenStax Introductory Statistics 2e, 12.5 Prediction, exercise 27