twenty different statistics students are randomly selected. for each of them, their body temperature (°c) is mea and their head circumference (cm) is measured.
a. for this sample of paired data, what does r represent, and what does $\
ho$ represent?
b. without doing any research or calculations, estimate the value of r.
c. does r change if body temperatures are converted to fahrenheit degrees?

c. the value of r is estimated to be $\square$, because it is likely that body temperature and strongly positively correlated.
e. choose the correct answer below.

$\bigcirc$ a. the value of r does not change, because r is not affected by relationships that are not linear
$\bigcirc$ b. the value of r does not change, because r is not affected by the choice of x or y.
$\bigcirc$ c. the value of r does not change, because r is not affected by converting all values of a variable to a different scale
$\bigcirc$ d. the value of r changes, because r is affected by converting all values of a variable to a different scale

Question

twenty different statistics students are randomly selected. for each of them, their body temperature (°c) is mea and their head circumference (cm) is measured.
 a. for this sample of paired data, what does r represent, and what does $\
ho$ represent?
 b. without doing any research or calculations, estimate the value of r.
 c. does r change if body temperatures are converted to fahrenheit degrees?

c. the value of r is estimated to be $\square$, because it is likely that body temperature and strongly positively correlated.
 e. choose the correct answer below.

$\bigcirc$ a. the value of r does not change, because r is not affected by relationships that are not linear
 $\bigcirc$ b. the value of r does not change, because r is not affected by the choice of x or y.
 $\bigcirc$ c. the value of r does not change, because r is not affected by converting all values of a variable to a different scale
 $\bigcirc$ d. the value of r changes, because r is affected by converting all values of a variable to a different scale

Accepted Answer

# Brief Explanations:
To determine the correct answer for part c, we analyze the properties of the correlation coefficient $ r $. The correlation coefficient measures the strength and direction of the linear relationship between two variables. Converting body temperatures from Celsius to Fahrenheit is a linear transformation (scaling and shifting the values). The correlation coefficient $ r $ is invariant under linear transformations of the variables (like changing the scale from Celsius to Fahrenheit) because it depends on the relative variation between the variables, not their absolute scale.

- Option A is incorrect because the question is about scale conversion, not linearity of the relationship.
- Option B is incorrect because the question is about scale conversion, not the choice of $ x $ or $ y $.
- Option C is correct because $ r $ is not affected by converting all values of a variable to a different scale (linear transformation).
- Option D is incorrect because $ r $ is not affected by scale conversion.

# Answer:
C. The value of $ r $ does not change, because $ r $ is not affected by converting all values of a variable to a different scale.

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