Question

Ben loves Thanksgiving and he cooks the family turkey every year. He has noticed that over the years the amount of people who show up for his Thanksgiving dinner tends to vary, and he was wondering if this was correlated with the size of the turkeys he cooks. He recorded the weight of the turkeys he cooked (in lbs.) and the amount of guests who showed up for diner for 12 randomly chosen Thanksgivings. When he was analyzing the data he decided to perform a Box Cox transformation and he derived a lambda equal to 0.891.

What transformation does this value of lambda suggest?
a. With a lambda close to 1. it looks like we should take the square root of y
b. With a lambda close to 1. it does not look like we need to re-express the data.
c. With a lambda close to 1, it looks like we should take the log of y
d. With a lambda close to 1. it looks like we should take the log of x.

Answer 1

The answer is "Option b".

Explanation:

Calculating the common Box-Cox Transformation:

`\lambda \ value \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Transformed \ data \ (Y')\\\\`

`-3 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Y^(-3) =(1)/(Y^3) \\\\ -2 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Y^(-2) =(1)/(Y^2) \\\\ -1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Y^(-1) =(1)/(Y^1) \\\\ -0.5 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Y^(-0.5) =(1)/(√(Y)) \\\\ 0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \log(Y)^(**) \\\\`

`0.5 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Y^(-0.5) =√((Y)) \\\\ 1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Y^(1) =Y \\\\ 2 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Y^(2) \\\\ 3 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Y^(3) \\\\`