Prediction (Optional) · Exercise 24

$$\begin{array}{ccccc}\text{State}& \text{No. of Letters in Name}& \text{Year Entered the Union}& \text{Rank for Entering the Union}& \text{Area in square miles}\\ \text{Alabama}& \text{7}& \text{1819}& \text{22}& \text{52,423}\\ \text{Colorado}& \text{8}& \text{1876}& \text{38}& \text{104,100}\\ \text{Hawaii}& \text{6}& \text{1959}& \text{50}& \text{10,932}\\ \text{Iowa}& \text{4}& \text{1846}& \text{29}& \text{56,276}\\ \text{Maryland}& \text{8}& \text{1788}& \text{7}& \text{12,407}\\ \text{Missouri}& \text{8}& \text{1821}& \text{24}& \text{69,709}\\ \text{New Jersey}& \text{9}& \text{1787}& \text{3}& \text{8,722}\\ \text{Ohio}& \text{4}& \text{1803}& \text{17}& \text{44,828}\\ \text{South Carolina}& \text{13}& \text{1788}& \text{8}& \text{32,008}\\ \text{Utah}& \text{4}& \text{1896}& \text{45}& \text{84,904}\\ \text{Wisconsin}& \text{9}& \text{1848}& \text{30}& \text{65,499}\end{array}$$
We are interested in whether the number of letters in a state name depends on 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 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 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.
(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 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 24