Please label each part E Part (i)Use the least squares line to estimate the gold medal time for the 2012 Summer Olympics. (Use your equation from part (d). Round your answer to two decimalplaces.)secDo you think that your answer is reasonable? Why or why not?Yes, because the estimate is positive.No, because 2012 is outside the domain of the least squares line. The following table gives the gold medal times for every other Summer Olympics for the women's 100 meter freestyle (swimming).YearTime (seconds)191282.2192472.4193266.8195266.8196061.2196860.0197655.65198455.92199254.64200053.8200853.1+ Part (a)O Part (b)Part (c)Part (d)Calculate the least squares line. Put the equation in the form of: ý = a + bx. (Round your answers to three decimal places.)+O Part (e)Find the correlation coefficient r. (Round your answer to four decimal places.)r =Is the decrease in times significant?YesNoO Part (f)Find the estimated gold medal time for 1924. (Use your equation from part (d). Round your answer to two decimal places.)secFind the estimated gold medal time for 1992. (Use your equation from part (d). Round your answer to two decimal places.)sec

Part (d) Let x represents year, and y represents the gold medal times. The regression analysis is conducted using EXCEL. The software procedure is given below: Enter the data. Select Data > Data Analysis >Regression> OK. Enter Input Y Range as Year. Enter Input X Range as Time. Click OK. The output using EXCEL is as follows: From the output, the intercept(a) is 603.430, and slope(b) is -0.276. The least square line is y^=603.430+(-0.276)x.Part (e) The correlation value is obtained using EXCEL. The software procedure is given below: Enter the data. Select Data > Data Analysis >Correlation> OK. Enter Input Range as A1:B12. Mark Labels in First Row. Click OK. The output using EXCEL is as follows: From the output, the correlation coefficient is -0.9512. Thus, the correlation coefficient r is -0.9512. Part (f) The estimated gold medal time for 1924 is, y^=603.430-0.276x=603.430-0.2761924=603.430-531.024=72.406≈72.41 Thus, the estimated gold medal time for 1924 is 72.41. The estimated gold medal time for 1992 is, y^=603.430-0.276x=603.430-0.2761992=603.430-549.792=53.638≈53.64 Thus, the estimated gold medal time for 1992 is 53.64. The estimated gold medal time for 2012 is, y^=603.430-0.276x=603.430-0.2762012=603.430-555.312=48.118≈48.12 Thus, the estimated gold medal time for 2012 is 48.12.