Question

Suppose that a tall child with an arm span of 120 cm and a height of 118 cm was added to the sample used in this study. What effect will this addition have on the correlation and the slope of the least-squares regression line?

a. Correlation will increase, and the slope will increase.

b. Correlation will increase, and the slope will stay the same.

c. Correlation will increase, and the slope will decrease.

d. Correlation will stay the same, and the slope will stay the same.

e. Correlation will stay the same, and the slope will increase.

Short answer

The correct option is (b).

Step-by-step solution

Given information and Explanation

It is given that $x$be as Arm span and $y$be the height.

And also,

$$\begin{gathered} \stackrel{⏜}{y}=6.4+0.93x \\ x=120 \\ y=118 \end{gathered}$$

Now, let us find the predicted value as:

$$\begin{gathered} \stackrel{⏜}{y}=6.4+0.93x \\ =6.4+0.93\left(120\right) \\ =118 \end{gathered}$$

As a result, the predicted and actual values are the same, indicating that the point will fall along the regression line. As a result, the data becomes more linear. As a result, the correlation will grow. And because this point has no effect on the regression line, the slope will remain unchanged.

Thus, option (b) is the correct option.