The ordered pairs below give the winning times (in seconds) of the women's 100-meter freestyle in the Olympics from 1984 through 2012. (Spreadsheet at LarsonPrecalculus.com) (Source: International Olympic Committee)
(1984, 55.92)
(1988, 54.93)
(1992, 54.64)
(1996, 54.50)
(2000, 53.83)
(2004, 53.84)
(2008, 53.12)
(2012, 53.00)
(a) Sketch a scatter plot of the data. Let y represent the winning time (in seconds) and let t = 84 represent 1984.
(b) Sketch the line that you think best approximates the data and find an equation of the line.
(c) Use the regression feature of a graphing utility to find the equation of the least squares regression line that fits the data.
(d) Compare the linear model you found in part (b) with the linear model you found in part(c).