1. What are the four rules to choose independent variables? 2. Discuss the consequence(s) of over-identification and under-specification.

Cholesterol Cholesterol in human blood is necessary, but too much can lead to health problems. There are three main types of cholesterol: HDL (high-density lipoproteins), LDL (low-density lipoproteins), and VLDL (very low-density lipoproteins). HDL is considered “good” cholesterol; LDL and VLDL are considered “bad” cholesterol. A standard fasting cholesterol blood test measures total cholesterol, HDL cholesterol, and triglycerides. These numbers are used to estimate LDL and VLDL, which are difficult to measure directly. Your doctor recommends that your combined LDL/VLDL cholesterol level be less than 130 milligrams per deciliter, your HDL cholesterol level be at least 60 milligrams per deciliter, and your total cholesterol level be no more than 200 milligrams per deciliter. (a) Write a system of linear inequalities for the recommended cholesterol levels. Let x represent the HDL cholesterol level, and let y represent the combined LDL VLDL cholesterol level. (b) Graph the system of inequalities from part (a). Label any vertices of the solution region. (c) Is the following set of cholesterol levels within the recommendations? Explain. LDL/VLDL: 120 milligrams per deciliter HDL: 90 milligrams per deciliter Total: 210 milligrams per deciliter (d) Give an example of cholesterol levels in which the LDL/VLDL cholesterol level is too high but the HDL cholesterol level is acceptable. (e) Another recommendation is that the ratio of total cholesterol to HDL cholesterol be less than 4 (that is, less than 4 to 1). Identify a point in the solution region from part (b) that meets this recommendation, and explain why it meets the recommendation.

Answer the following questions. 5. What is the term for the arrangement that selects r objects from a set of ii objects when the order of the r objects is not important? What is the formula for calculating the number of possible outcomes for this type of arrangement?

Atlantic hurricanes form off the western coast of Africa. As warm moist air rises, it begins to rotate around a low- pressure system. This rotation is sustained by warm ocean temperatures and a central low pressure. Once a sustained wind speed of 74 miles per hour is reached, the storm is considered a hurricane. As man-made climate change continues to increase the temperature of the Earth's oceans, it is expected that the strength of hurricanes will Typically, a lower central pressure within a hurricane's eye is associated with a higher wind speed. Here, statistical software (R/RStudio) will be used to explore this relationship by applying linear regression methods. Using a database of landfalling hurricanes in the United States, a linear regression will be used to correlate the central pressure of each hurricane to its maximum sustained wind speed. increase. Regression Plot y=942.196-0.884*x R^2=0.768 ----- ----------- -. •... •. 980 1000 940 960 900 920 Independent Variable (x)…