You may use TI calculators, Excel, or any other appropriate technology to find your answers. When calculating values of the correlation coefficient and values in the regression equation, always round to the nearest thousandth (three decimal places). 1. The table below shows the gold medal times for every summer Olympics for the women's 100-meter freestyle swimming event. a. Let x = the number of years since 1912. Fill in the table Year X = years Time to find the corresponding values of x for each year. since 1912 seconds) 1912 82.2 b. Find the equation of the line of best fit where x = the 1924 72.4 number of years since 1912 and let y = the time in seconds. 1932 66.8 1960 61.2 1968 60.0 c. State the value of the correlation coefficient. 1976 55.65 1984 55.92 d. Interpret the correlation coefficient. In other words, what type of relationship exists (positive or negative ) and what 1992 54.64 does that mean about the speed of swimmers over time? 2000 53.8 2008 53.1 2012 53.00 e. What is the slope of the line of best fit? Write a sentence 2016 52.70 to interpret the slope in the context of the problem. f. Use the equation of the line of best fit to predict the gold medal time for the 2020 summer Olympics. Show work using the equation and round to the nearest hundredth. Compare this to the true time of 51.96 sec from Emma Mckeon of Australia. How well did the equation predict the true value? g. Can this equation do a good job of predicting swim times forever? How can you tell? Consider what you know about interpolation and extrapolation from our videos. Consider choosing more years and experimenting with the equation to answer this question.2. A biologist is studying how water temperature affects feeding habits of a certain species of fish. She collects measurements from several days, collecting data on the water temperature and the quantity of live food the fish has consumed per day (in ke). The data appear in the table. Let x represent the temperature in ("C) and let y represent the food consumption rate in kg day. Temperature ('C) 15 34 26 15 20 22 35 19 31 25 30 Consumption rate (kg day) 0.1 0.7 0.2 0.6 0.5 1.6 |0.4 1.4 0.6 0.8 a. Use Excel to create a scatter plot of the data. Copy and paste the image from Excel into this document. Label axes appropriately. b. Find the correlation coefficient, r. c. Write the equation of the regression equation (least-squares line). Record your answer here. d. Interpret the relationship between these variables. Is the relationship positive or negative? Strong or weak? Write a sentence to interpret what that means in the context of the problem. e. What is the slope of the least-squares line? Write a sentence to interpret the slope. f. Use the equation to predict the consumption rate for a fish in water at each of the following temperatures. Show work using the equation. Do you think the least-squares line is reliable in predicting these results? Explain. 28'C 40-C g. Use the equation to predict the water temperature if the fish consumed 1 keg of food in a day.Refer to the introduction videos describing correlation. Remember that correlation does not imply conisation In each example, a pair of variables is given that have a correlation Determine at least one lurking variable that could be influencing this relationship. In other words, what reasons might explain the relationship (other than cause-and effect or just coincidence)? Be creative and brainstorm 3. A college hosts an optional "welcome day" for incoming freshman at the beginning of each semester. At this event, students meet faculty, attend workshops in topics related to college success, and have a picnic lunch and party on campus. It is found that students who attend welcome day are more likely to graduate and have higher GPAs. An administrator concludes that if students attend welcome day, this causes an increase in student success. 4. Researchers found that women who don't work during pregnancy tend to have healthier babies. They conclude that going to work while pregnant can have a harmful impact on the health of the child