Part 1

a. Report the regression equation, using the words "Height" and "Armspan," not x and y.

From the linear regression equation format $y = a + bx$, where:

• $a = 17.66$ is the y-intercept,
• $b = 2.23$ is the slope of the regression line,
• The equation can be written as:

Predicted Armspan = 17.66 + 2.23 * Height

Correct answer:

• B. Predicted Armspan = 17.66 + 2.23 * Height

Part 2

b. Determine the corresponding values and verify the slope by using the formula:

$b = r \cdot \frac{s_y}{s_x}$

Where:

• $r$ is the correlation coefficient,
• $s_y$ is the standard deviation of Armspan,
• $s_x$ is the standard deviation of Height.

From the given data:

• $r = 0.919$ (correlation coefficient),
• $s_y = 8.00$ (standard deviation of Armspan),
• $s_x = 3.30$ (standard deviation of Height).

Using the formula:

$b = 0.919 \cdot \frac{8.00}{3.30}$

Now, let's compute the value for $b$.

$b = 0.919 \cdot 2.4242 \approx 2.23$

Thus, the slope $b$ is approximately 2.23.

Summary of the values:

• r = 0.919 (round to three decimal places)
• $s_y = 8.00$ (round to two decimal places)
• $s_x = 3.30$ (round to two decimal places)
• b = 2.23 (round to two decimal places)

Let me know if you'd like further details or have any other questions!

Related Questions:

1. How would the regression equation change if the standard deviation of Armspan were larger or smaller?
2. What does the correlation coefficient $r = 0.919$ tell us about the relationship between Height and Armspan?
3. How do you interpret the y-intercept (17.66) in the context of this regression model?
4. How does increasing the sample size impact the accuracy of the regression model?
5. How can the standard deviations of Height and Armspan affect the slope of the regression line?

Tip: A higher correlation coefficient (closer to 1 or -1) generally means a stronger linear relationship between the two variables.