Prediction · Exercise 24

gives the gold medal times for every other Summer Olympics for the women’s 100-meter freestyle (swimming).

$$\begin{array}{cc}\text{Year}& \text{Time (seconds)}\\ \text{1912}& \text{82.2}\\ \text{1924}& \text{72.4}\\ \text{1932}& \text{66.8}\\ \text{1952}& \text{66.8}\\ \text{1960}& \text{61.2}\\ \text{1968}& \text{60.0}\\ \text{1976}& \text{55.65}\\ \text{1984}& \text{55.92}\\ \text{1992}& \text{54.64}\\ \text{2000}& \text{53.8}\\ \text{2008}& \text{53.1}\\ \text{2016}& \text{52.7}\end{array}$$

(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. Is the decrease in times significant?
(f) Find the estimated gold medal time for 1932. Find the estimated time for 1984.
(g) Why are the answers from part f different from the chart values?
(h) Does it appear that a line is the best way to fit the data? Why or why not?
(i) Use the least-squares line to estimate the gold medal time for the next Summer Olympics. Do you think that your answer is reasonable? Why or why not?

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Introductory Statistics 2e · §12.5 Prediction · Exercise 24