Chapter 3.2, Problem 74E

To determine

To find: The correlation between height and arm span by looking at the regression equation

Answer to Problem 74E

It is greater than 0.

Explanation of Solution

Given:

The regression line is: $\widehat{y}=6.4+0.93x$

The relationship between the slope and the correlation coefficient is given by:

  $b=r\left(\frac{s_y}{s_x}\right)$

Here, b is the slope of the least squares line, r is the sample correlation coefficient, and $s_x$ and $s_y$ are the sample standard deviations of the variables X and Y , respectively.

Since the standard deviation of any random variable cannot be a negative value, the ratio $\left(\frac{s_y}{s_x}\right)$ is always positive. So, the slope of the least squares line is directly proportional to the sample correlation coefficient. The slope and the correlation coefficient will always have the same sign.

Here, the slope of the least square line is positive. Thus, correlation will also be positive, that is, greater than 0.

Hence, the correct option is (a).