MATH 225N Week 8 Assignment: Correlation and Causation, Exams of Mathematics

Download MATH 225N Week 8 Assignment: Correlation and Causation and more Exams Mathematics in PDF only on Docsity! MATH 225N Week 8 Assignment: Correlation and Causation Understand the difference between correlation and causation Question True or False: The more samples taken in a scientific study, the longer the amount of time it will take to complete the research on the samples. Although there are other factors that affect study time, such as experience and equipment, increasing the number of samples will cause an increase in research time. Correct! You nailed it. Understand the difference between correlation and causation Question Suppose that a large controlled experiment tests whether caffeine improves reaction times. A very large number of randomly selected participants are randomly given identical-seeming pills with varying doses of caffeine (including none) and then given tests of reaction times under the same conditions. The experiment finds a strong negative correlation between caffeine dose and reaction time. (Note that lower reaction times are better.) Correct answer: There is evidence that caffeine causes lower (better) reaction times. Correlation alone does not prove causation, but this scenario provides more evidence than just correlation between two variables. Since the data were obtained from an appropriately randomized controlled experiment, a correlation can be used as evidence of a causal relationship. Since all other variables were controlled, there is no third variable that could be associated with caffeine that actually causes differences in reaction times. Yes that's right. Keep it up! Interpret the slope and y-intercept of the least squares regression line Question Which of the following situations could have a regression line with a negative y- intercept? Select all that apply: Great work! That's correct. • The present value of an insurance policy as a function of the age of the ensured person if the person purchases the policy when he or she is 50 years old. • • The number of millions of barrels of oil in an oil field as a function of the number of years the oil field has been in production. • • The value of a Fortune-500 company, founded in the year 1990, as a function of the number of years after the year 2010. • • The value of a rail locomotive as a function of the number of years since it was put into service. Interpret the slope and y-intercept of the least squares regression line Question Which of the following situations would have data sets or plots that could have a regression line with a positive slope? Select all that apply. Great work! That's correct. Correct answer: The cumulative number of ships launched by ship builders as a function of the number of months since the start of the year The number of cars produced as a function of the number of days since the end of the last strike. The total shipping orders that are backlogged as a function of the number of ships in drydock. The slope is related to the increase or decrease of the dependent variable as a function of the independent variable. If the dependent variable can increase, then the slope can be positive, such as with the cumulative number of ships launched. Interpret the slope and y-intercept of the least squares regression line Question Which of the following situations could produce data sets or plots would have a regression line with a negative slope? Select all that apply. Well done! You got it right. Correct answer: The number of miles a ship travels each year as a function of the number of years since it was launched. the number of voyages a ship can make per year as a function of the length (in days) of each voyage. The slope is related to the increase or decrease of the dependent variable as a function of the independent variable. If the dependent variable can decrease, then the slope can be negative, such as with the number of cats born each year. .