3.3 Transforming to Achieve Linearity

What is the purpose of using transformations like powers, roots, and logarithms on data?

• To remove data points

• To make data more complex

• To create a linear model from nonlinear data

• To make data nonlinear

In the fishing tournament example, what transformation was applied to the lengths of the fish (x-values)?

• Doubling the lengths

• Square root the lengths

• Logarithm of the lengths

• Cubing the lengths

Why do we take the log of both variables in a power model?

• To make the data more colorful

• To create a linear pattern

• To increase the data size

• To make the data disappear

Which of the following would provide evidence that a particular model describes the nonlinear relationship between a response variable y and an explanatory variable x?

• A residual plot of the transformed data looks randomly scattered with no leftover curved pattern.

• A residual plot of the transformed data displays a curved pattern.

• A residual plot of the transformed data looks approximately linear.

• The value of r-squared for the least-squares regression line of the transformed data is close to zero.

• The value of r-squared for the least-squares regression line of the transformed data is less than 0.5.

Rheumatoid Arthritis patients are often treated with large quantities of aspirin. The concentration of aspirin in the bloodstream increase for a period of time after the drug is administered and then decreases in such a way that the amount of aspirin remaining is a function of the amount of time that has elapsed since peak concentration. The table shows the data for a particular arthritis patient who has taken a large dose of aspirin. The residual plot shows a clear curved pattern. Which of the following transformed scatterplots appears to be the best choice to perform to make the data most linear?

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• No transformation is best. Just using the linear model for the curved data is best.

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