Answer :
Final answer:
The estimated slope of the linear regression line for predicting height based on shoulder girth is 0.5953 when using the provided correlation coefficient, standard deviation of height, and standard deviation of shoulder girth.
Explanation:
The student asked for the estimated slope of the linear regression line for predicting height based on shoulder girth from a sample of adults in California. To calculate the slope (b) in a linear regression, you can use the formula:
b = r * (Sy/Sx)
where r is the correlation between the two variables, Sy is the standard deviation of the dependent variable (height, in this case), and Sx is the standard deviation of the independent variable (shoulder girth, in this case).
Given the data:
- Correlation (r) = 0.679
- Standard deviation of height (Sy) = 9.3 cm
- Standard deviation of shoulder girth (Sx) = 10.61 cm
Plug in the values to the formula:
b = 0.679 * (9.3 cm / 10.61 cm)
b = 0.679 * 0.8764
b = 0.5953 cm
So, the estimated slope of the linear regression line for predicting height based on shoulder girth is approximately 0.5953.