Question
Which paired data will show a nonlinear​ association?
Question content area bottom
Part 1
Select all that apply.
A.
Area and side length of a square
B.
Age and number of siblings
C.
Height of a bouncing ball and time
D.
Age and weight of puppies
E.
Amount of money earned and length of hair
Question content area bottom
Part 1
Select all that apply.
A.
Area and side length of a square
B.
Age and number of siblings
C.
Height of a bouncing ball and time
D.
Age and weight of puppies
E.
Amount of money earned and length of hair
Answers
GPT-4o mini
To identify which paired data shows a nonlinear association, let's analyze each option:
A. **Area and side length of a square**: This has a quadratic relationship \(A = s^2\), where \(A\) is the area and \(s\) is the side length. This is nonlinear.
B. **Age and number of siblings**: This data does not inherently indicate a clear relationship, but generally, the number of siblings does not increase or follow a predictable pattern with age, likely leading to a nonlinear association.
C. **Height of a bouncing ball and time**: The height of a bouncing ball decreases over time in a nonlinear fashion due to the effects of gravity and energy loss with each bounce. This is nonlinear.
D. **Age and weight of puppies**: Typically, there is a nonlinear relationship during the early stages of a puppy's development as they grow rapidly. As they age, their growth rate slows, creating a nonlinear association.
E. **Amount of money earned and length of hair**: There is no expected consistent relationship between these two variables. This is likely to be nonlinear without a clear association.
Based on the analysis above, the options that show a nonlinear association are:
- A. Area and side length of a square
- C. Height of a bouncing ball and time
- D. Age and weight of puppies
So, the answer would be options A, C, and D.
A. **Area and side length of a square**: This has a quadratic relationship \(A = s^2\), where \(A\) is the area and \(s\) is the side length. This is nonlinear.
B. **Age and number of siblings**: This data does not inherently indicate a clear relationship, but generally, the number of siblings does not increase or follow a predictable pattern with age, likely leading to a nonlinear association.
C. **Height of a bouncing ball and time**: The height of a bouncing ball decreases over time in a nonlinear fashion due to the effects of gravity and energy loss with each bounce. This is nonlinear.
D. **Age and weight of puppies**: Typically, there is a nonlinear relationship during the early stages of a puppy's development as they grow rapidly. As they age, their growth rate slows, creating a nonlinear association.
E. **Amount of money earned and length of hair**: There is no expected consistent relationship between these two variables. This is likely to be nonlinear without a clear association.
Based on the analysis above, the options that show a nonlinear association are:
- A. Area and side length of a square
- C. Height of a bouncing ball and time
- D. Age and weight of puppies
So, the answer would be options A, C, and D.