Prediction · Exercise 25

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

OpenStax, Introductory Statistics 2e · §12.5 Prediction · Exercise 25