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MATH 220

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Apr 3, 2024

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Math 220 Team Sheet Spring 2023 In-Class Group Activity: Chapter 11 SECTION: 15 GROUP #: 16 TEAM MEMBERS: 1. (leader) Carolyn Wilson 2. Trey Campbell (present). 3. Jamie Del Cid (present) 2. A study found a high positive correlation (r = .921) between the size of the hospital where a patient’s surgery was performed and the length of the patient’s stay following surgery. (x = number of beds in the hospital, y = number of days following surgery before the release from the hospital) Is the most reasonable explanation for this correlation cause-and-effect or a hidden cause? If it is not cause-and-effect, suggest a reasonable hidden cause. Hidden cause because there are other factors such as longer surgeries, stays, or even complications 3. Mortgage payments: The following table presents interest rates, in percent, for 30-year and 15-year fixed- rate mortgages, for January through December 2018. a. Find the least-squares regression line for predicting the 15-year rate from the 30-year rate. b0= -.286 b1 = .942 r= .994 ŷ = -.286 + .942x y= 15 years x= 30 years b. Describe the relationship between the 30-year and the 15-year fixed-rate mortgages in context. The correlation coefficient r=.994. Indicates a strong, positive, linear relationship between the 15- and 30-year rates. c. Is it possible to interpret the y-intercept? Explain. Yes because it is within the range of this graph d. What does the slope of the regression line represent in context?
The slope is .942 which is very close to 1 and indicates a strong positive correlation between both variables. For every 1 increase in the 15 years, the 30 years increases by .942. e. If the 30-year rate differs by 0.3 percent from one month to the next, by how much would you predict the 15-year rate to differ? Because they are directly correlated if the 30- year differs by .3 percent the 15- year should be changing at the same rate f. Predict the 15-year rate for a month when the 30-year rate is 4.5%. ŷ = -.286 + .942(4.5) =3.95 The 15-year rate should be 3.95% when the 30-year rate is 4.5%. 4. Carbon dioxide (CO2) is produced by burning fossil fuels such as oil and natural gas, and has been connected to global warming. The following table presents the average amounts (in metric tons) of CO2 emissions for the years 1990 – 2006 per person in the United States and per person in the rest of the world. The SPSS output including the scatterplot of U.S. carbon dioxide emissions (y) versus non-U.S. emissions (x) and the model summary are shown below. a. What is the response variable? U.S. carbon dioxide emissions is the response variable. b. What is the explanatory variable? Non-US carbon dioxide emissions is the explanatory variable c. What is the correlation coefficient value? What does it tell us about the relationship between U.S. carbon dioxide emissions and non-U.S. emissions? The correlation coefficient r = -.516. It has a moderately negative linear correlation. d. As developing countries modernize, their use of fossil fuels increases. Countries that are already developed strive to reduce emissions. How does this fact explain the negative correlation coefficient between U.S. carbon dioxide emissions and non-U.S. emissions? The non-U.S. emissions are lower but increasing due to the lack of effort to reduce remission while the U.S. emissions are higher because they were already established but are getting lower as time goes on.
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