Answer :
a) Estimated slope: 0.5713 cm/cm
b) Estimated intercept: 98.5703 cm
1. Formula for slope and intercept:
The slope (b) and intercept (a) of the linear regression line can be estimated using the following formulas:
Slope (b):
b = r * (Sy / Sx)
where:
r is the correlation coefficient (0.677 in this case)
Sy is the standard deviation of height (9.22 cm)
Sx is the standard deviation of shoulder girth (10.97 cm)
2. Calculations:
Slope (b):
b = 0.677 * (9.22 cm / 10.97 cm) ≈ 0.57125 cm/cm
Intercept (a):
a = 171.02 cm - 0.57125 cm/cm * 108.56 cm ≈ 98.5703 cm
3. Answer:
Therefore, the estimated slope of the linear regression for predicting height based on shoulder girth is 0.5713 cm/cm (rounded to 4 decimal places). This means that for every 1 cm increase in shoulder girth, we can expect an average increase of 0.5713 cm in height.
The estimated intercept of the linear regression is 98.5703 cm (rounded to 4 decimal places).
Complete question:
Suppose that shoulder girth length and height are collected from a random sample of adults of 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 108.56 cm with a standard deviation of 10.97 cm. The mean height is 171.02 cm with a standard deviation of 9.22 cm. The correlation between height and shoulder girth is 0.677. All answers must be rounded to 4 decimal places. a) What is the estimated slope of the linear regression for predicting height based on the shoulder girth: b) What is the estimated intercept of the linear regression for predicting height based on the shoulder girth:
