Question
Emily wants to determine the relationship between the number of people in a household (x) and the last 4 digits of their phone number (y). She randomly selects 100 households in her town and examines the data.
What is the ,begin emphasis,best,end emphasis, estimate of the correlation coefficient between x and y?
What is the ,begin emphasis,best,end emphasis, estimate of the correlation coefficient between x and y?
Answers
GPT-4o mini
The scenario you've described involves examining the relationship between two seemingly unrelated variables: the number of people in a household (x) and the last four digits of their phone number (y).
Given that the last four digits of a phone number are typically assigned randomly and do not follow any systematic pattern in relation to the number of people residing in a household, it is reasonable to conclude that there would be no meaningful correlation between these two variables.
Thus, the best estimate of the correlation coefficient \( r \) between \( x \) and \( y \) would be close to:
\[
r \approx 0
\]
This indicates no linear relationship. In practice, after calculating the correlation from a data set like this, we would expect a value very near 0, supporting the intuition that there is little to no correlation between the household size and the last four digits of their phone numbers.
Given that the last four digits of a phone number are typically assigned randomly and do not follow any systematic pattern in relation to the number of people residing in a household, it is reasonable to conclude that there would be no meaningful correlation between these two variables.
Thus, the best estimate of the correlation coefficient \( r \) between \( x \) and \( y \) would be close to:
\[
r \approx 0
\]
This indicates no linear relationship. In practice, after calculating the correlation from a data set like this, we would expect a value very near 0, supporting the intuition that there is little to no correlation between the household size and the last four digits of their phone numbers.