| State | # letters in name | Year entered the Union | Ranks 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 there is a relationship between the ranking of a state and the area of the state.
- What are the independent and dependent variables?
- What do you think the scatter plot will look like? Make 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 areas for Alabama and for Colorado. Are they close to the actual areas?
- Use the two points in part f to plot the least-squares line on your graph from part b.
- Does it appear that a line is the best way to fit the data? Why or why not?
- Are there any outliers?
- 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?
- Delete “Hawaii” and substitute “Alaska” for it. Alaska is the forty-ninth, state with an area of 656,424 square miles.
- Calculate the new least-squares line.
- 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?
- Do you think that, in general, newer states are larger than the original states?
OpenStax Introductory Statistics 2e, 12.6 Outliers, exercise 26