Question

question 9
1 pts
a researcher studies the linear relationship between daily screen exposure and stress levels. daily screen exposure is originally recorded in hours, and this results in a correlation of r = 0.63. a second researcher decides that it would be better to report daily screen exposure in seconds. the second researcher converts all daily screen exposure times to seconds and then re-computes r. which one of the following is the most accurate statement about how r will change once hours are converted to seconds?

the value of r will remain equal to 0.63.

the value of r will change only if the slope changes.

the value of r will change because a conversion from hours to seconds is considered a nonlinear transformation.

the value of r will increase in magnitude because seconds have a larger overall range of values than hours.

the value of r will decrease in magnitude because converting to seconds will extend the x-axis and result in more scatter in the data.

Explanation:

The correlation coefficient \( r \) measures the strength and direction of the linear relationship between two variables. It is invariant under linear transformations (like converting hours to seconds, which is a linear scale change: \( \text{seconds} = 3600 \times \text{hours} \)). Linear transformations do not change the shape of the relationship or the relative positions of data points, so \( r \) remains the same. The other options are incorrect: slope change isn't the only factor (and \( r \) doesn't depend on slope alone), converting hours to seconds is linear, and range or axis extension doesn't affect \( r \)'s magnitude.

Answer:

The value of \( r \) will remain equal to 0.63.