Chapter 10 - Re-expressing Data: Get It Straight!

Question 1

Re-expression

Answer 1

We do this to data when we take a logarithm, square root, reciprocal, or some other mathematical operation on all values of a variable.

Question 2

Ladder of Powers

Answer 2

This places in order the effects that many re-expressions have on the data.

Question 3

What is meant by re-expressing data?

Answer 3

Making the data more suitable for analysis.

Question 4

One of the goals of re-expressing data is to make the distribution appear more symmetric. Why is this advantageous?

Answer 4

It is easier to summarize the center of data and it can make distribution look more like a normal model, which means you can use the 68-95-99.7 rule.

Question 5

Another goal of re-expressing data is to make the spread of several groups more alike. Why is this advantageous?

Answer 5

Groups that share a common spread are easier to compare.

Question 6

Why is it advantageous to make the form of a scatter plot more nearly linear?

Answer 6

Makes scatter plot easier to describe and also makes it possible to fit linear model once the relationship is straight.

Question 7

What type of data often benefits from re-expression by squaring values?

Answer 7

Unimodal distributions skewed to the left.

Question 8

What type of data often benefits from re-expression by taking the square root of values?

Answer 8

Counted Data

Question 9

What type of data often benefits from re-expression by taking the logarithm of values?

Answer 9

Data that can not be negative. Usually values that grow by percentage rates. When re-expressing, start with logs and then look at the residual plot to see which direction to go in.

Question 10

What type of data often benefits from re-expression by taking the reciprocal of values?

Answer 10

Data that uses measurements of rate.

Question 11

If your data contain zeroes, what must you do before re-expressing using logarithms or reciprocals? Explain.

Answer 11

Try adding small constant to all values before finding logs. You use logs because if you take y to the 0th power, you get 1. Every value would be same, so that is why you add a small constant before.

Question 12

If a scatterplot of the x-values vs. the logarithm of the y-values appears to be linear, what type of relationship is there between the original x- and y-values?

Answer 12

Exponential.

Question 13

Rewrite ^

y = ab^x.

Answer 13

y = a + b ln (x)

Question 14

If a scatterplot of the logarithm of the x- values vs. the logarithm of the y-values appears to be linear, what type of relationship is there between the original x- and y-values?

Answer 14

Power

Question 15

Rewrite ^

y = ax^b

Answer 15

log y = a+bx

Question 16

If a scatterplot of the logarithm of the x-values vs. the y-values appears to be linear, what type of relationship is there between the original x- and y-values?

Answer 16

logarithmic

Question 17

Rewrite ^

y = a + b ln(x)

Answer 17

log y = a + b log (x)

Question 18

Re-expression

Answer 18

Straightening bent relationships to make them look easier to think about by our methods. Re-expression doesn’t change the data but rather changes the way we look and think about it to make it more suitable for analysis.