The table below shows the winning times (in seconds) for the men's and women's 100-meter runs in the Summer Olympics from 1928 to 2016.

(a) Display the data in a scatter plot, calculate the correlation coefficient \(r\), and describe the type of correlation.

(b) At \(\alpha=0.05\), is there enough evidence to conclude that there is a significant linear correlation between the winning times for the men's and women's 100 -meter runs?

(c) Find the equation of the regression line for the data. Draw the regression line on the scatter plot.

(d) Use the regression equation to predict the women's 100-meter time when the men's 100 -meter time is 9.90 seconds.

Transcribed Image Text:

Men, x 10.80 10.38 10.30 10.30 10.79 10.62 10.32 Women, y 12.20 11.90 11.50 12.20 11.67 11.82 11.18 Men, .x 10.06 9.95 10.14 10.06 10.25 9.99 9.92 Women, y 11.49 11.08 11.07 11.08 11.06 10.97 10.54 Men, x 9.96 9.84 9.87 9.85 9.69 9.63 9.81 Women, y 10.82 10.94 10.75 10.93 10.78 10.75 10.90