Question

3) The table gives the gold medal times for every other Summer Olympics for the women's 100-meter freestyle swimming. Year 1912 1924 1932 Time (seconds) 82.2 72.4 66.8 1952 1960 1968 1976 66.8 61.2 60.0 55.65 55.92 54.64 53.8 (a) Use the Rossman Chance applet to find the least squares line. Put the equation in the form of: y = a + bx. (b) Find the estimated gold medal time for 1932. Find the estimated time for 1984. (c) Why are the answers from part f different from the chart values? (d) Does it appear that a line is the best way to fit the data? Why or why not? (e) 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? 1984 1992 2000 2008 53.1 Solution to (a): I Solution to (b): Solution to (c): Solution to (d): Solution to (e):

Answer 1

c) The regression line is the fitting line. The values from the regression line will not be same as of chart values, but the values will be nearly equal. d) Yes, the line is the best way to fit this data. of a graph is drawn between years and time, we can observe that the points almost form a straight line. e) Next , Summer Olympics 9016 - 1900- x=116 y : 49.78516 - 0.2756(116) Y = 44.8152 Answer is reasonable, as it is least when conepared previous year