YMS Chapter 4: More on TwoVariable 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?
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 Spring '07
 Molina
 Statistics, Exponential Function, Derivative, Linear function, power function

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