Activity #4 (14 Points): The data and scatter plot below represent the winning times in the Women's 100 meter freestyle swimming event in each summer Olympic games from 1948 to present (accessed Jan 25, 2018 from: https://www.olympic.org/swimming/100m-freestyle-women). Years have be scaled to "years after 1900". Years after Time Year 1900 (seconds] Women's Olympic Swimming 1948 48 56.3 Winning Times 100 meter Freestyle 1952 52 66.8 70 1956 56 62 68 1960 60 51.2 66 1964 64 59.5 1968 68 50 62 1972 72 58.59 1976 65.65 58 1980 80 54.79 56 1984 84 55.92 1988 88 54.93 54 1992 92 54.64 52 1996 96 $4.5 44 48 52 56 60 64 68 72 76 80 84 88 92 96 100 104 108 112 116 120 2000 53.83 Years After 1900 2004 104 53.84 2008 108 53.12 2012 112 53 2016 116 52.7 a. A scatter plot of the data is shown. Notice that years after 1900 are on the horizontal axis and winning times are on the vertical axis. Describe the relationship between the two variables shown on the scatter plot (include pattern and association) (2 points) b. Use technology to find the least squares regression line and the correlation coefficient. (3 points) c. Identify the slope in your least squares regression line and describe what it represents (using appropriate units). (2 points) d. Is a linear model a good fit for this data set? Why or why not (use the correlation coefficient table to justify your answer)? (2 points) e. Use your linear model to estimate the winning time in the 1996 Olympics (96 years after 1900). Compare your estimate to the actual value in the table above. (2 points) f. Use your linear model to estimate the winning time in the 2032 Olympics. Do you think this prediction is reasonable? Why or why not? (3 points)