Data were collected on two variables, x and y, to create a model to predict y from x. A scatterplot of the collected data revealed a curved pattern with a possible cubic relationship (y=ax^3, where a is a constant) between the variables. Which of the following transformations would be most appropriate for creating linearity between the variables?

A - Taking the cube of y
B - Taking the cube root of y
C - Taking the cube root of both y and x
D - Taking the log of y
E - Taking the log of both y and x

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andromache andromache · Answer 1 · 2020-10-18T07:55:08+02:00

Answer:

B - Taking the cube root of y

Step-by-step explanation:

Data provided in the question

y = ax^3

Based on the above information

Now we take the cube root of y

So, it would be calculated below:

y1/3 = a1/3 × x

So

As it can seen by the above equation there is a linear relationship between the cube root of y and x

Therefore, the correct option is B.

Hence, all the other options are wrong

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MrRoyal MrRoyal · Answer 2 · 2021-10-08T11:27:55+02:00

Linearity is the concept used to describe linear relationships between variables.

The appropriate method for creating linearity between the variables is: (e) Taking the log of both y and x

The function is given as:

[tex]\mathbf{y = ax^3}[/tex]

The function is a power function (i.e. cube of x)

To create linearity between power function, we simply take the logarithms of both variables

So, we have:

[tex]\mathbf{\log(y) = a\log(x^3)}[/tex]

Apply law of logarithm

[tex]\mathbf{\log(y) = 3a\log(x)}[/tex]

Hence, the appropriate method for creating linearity between the variables is: (e) Taking the log of both y and x

Read more about linearity between variables at:

https://brainly.com/question/11496246