AP Statistics Chapter 10: Re-expressing Data

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?

Exponential.

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

Groups that share a common spread are easier to compare.

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

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.

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

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

What is meant by re-expressing data?

Making the data more suitable for analysis.

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?

Power

Re-expression

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.

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

Counted Data

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

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.

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

Data that uses measurements of rate.

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

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.

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

Unimodal distributions skewed to the left.

Rewrite ^ y = a + b ln(x)

^ log y = a + b log (x)

Rewrite ^ y = ax^b

^ log y = a+bx

Rewrite ^ y = ab^x.

^ y = a + b ln (x)

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?

logarithmic