Suppose that shoulder girth and height are collected from a random sample of adults in California. In the data set, the minimum shoulder girth is 85 cm and the maximum shoulder girth is 139 cm. The mean shoulder girth is 108.17 cm with a standard deviation of 10.61 cm. The mean height is 171.63 cm with a standard deviation of 9.3 cm. The correlation between height and shoulder girth is 0.679.

What is the estimated slope of the linear regression for predicting height based on shoulder girth?

Note: All answers must be rounded to 4 decimal places.

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.