Chapter 3.2, Problem 76E

To determine

To find: the correlation between height and arm span

Answer to Problem 76E

The correlation between height and arm span is Greater than zero (option a)

Explanation of Solution

Given:

1. Greater than zero
2. Less than zero
3. 0.93.
4. 6.4.
5. Can’t tell without seeing the data.

Calculation:

Measurements on young children in Mumbai, India, found a least-squares line for predicting height Y from arm span X.

Measurements are in centimeters (cm).

From the given regression line, we can see that the slope of regression line is 0.93 which is positive.

We know that,

  $b=r\times \frac{s_y}{s_x}$

Where ris the correlation coefficient, $s_x$ and $s_y$ is the standard deviations of variables X and Y. As the standard deviations are always positive, the sign of the slope is same as the sign of the correlation coefficient

In the given regression line, as the sign of the slope is positive, hence, we can say that the sign of the correlation coefficient is also positive.

Conclusion:

Therefore, option (a) is the correct one.