YMS Chapter 4 - YMS Chapter 4: More on Two-Variable Data...

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YMS Chapter 4: More on Two-Variable Data Q1. In the example at the beginning of this chapter, a plot of the log of brain weight as a function of the log of body weight provides a “better fit” for the observed data than a simple plot of brain weight as a function of body weight. What is meant by better fit? (This is also the answer to the question, what are we trying to do (at least in this course) when we transform data?) Q2. Can you figure out why we would want to transform data so as to get a more linear relationship? Q3. True or false: if we have a curvilinear function, and we want to straighten it out to make a linear function, we can’t do that by multiplying or dividing by constants or adding or subtracting constants (i.e. by using linear transformations). Q4. What are the transformations that are most commonly used, other than linear transformation? Q5. What is the definition of a monotonic function? Q6. Is it kosher to speak of a function as being, for example, monotonic increasing over part of the domain of x, and monotonic decreasing over another part? If so, can you give an example? Q7. True or false: There are often two steps in tranformation. The second is to apply a power or logarithmic function that simplifies the data. The first is to use a linear transformation, such as adding a constant, that makes the values all positive, so that the function applied in the second step will be defined and monotonic increasing. Q8. How is the ladder of power functions useful? Q9. Linear growth is to adding a fixed amount per unit time as exponential growth is to ______ by a fixed amount per unit time. Q10. If the number of a certain type of bacteria doubles every two hours, is that linear growth or exponential growith? Q11. Increasing everyone’s salary by a certain percentage is to ______ growth as increasing everyone’s salary by the same dollar amount is to _______ growth. Q12. Suppose we have a function y=ab^x, where a and b are constants and x is the explanatory or independent variable, and y is the response or dependent variable. Is this an example of an exponential function, or a power function?
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Q13. Suppose we have a function y=ax^b, where a and b are constants and x is the explanatory variable and y is the response variable. Is this an example of an exponential function, or a power function? Q14. If y is an exponential function of x, plotting what function of y versus x should result in a linear graph? Q15. Suppose you do a regression of the log (base 10) of y versus x, and you get a nice linear scatterplot and a high coefficient of determination (r^2) when you do a regression. Now you can use this linear relationship for prediction. Suppose someone (like a test- maker) asks you what the predicted value is of y (not log y) for a given value of x. How would you find it? Q16. If a variable grows exponentially, its logarithm grows how?
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This note was uploaded on 04/06/2008 for the course MATH 101 taught by Professor Molina during the Spring '07 term at Saint Mary's University Texas.

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YMS Chapter 4 - YMS Chapter 4: More on Two-Variable Data...

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