Question

7.20 Body measurements, Part III. Exercise 7.13 introduces data on shoulder girth and height of a group of individuals. The mean shoulder girth is 107.30 cm with a standard deviation of 10.34 cm. The mean height is 171.14 cm with a standard deviation of 9.41 cm. The correlation between height and shoulder girth is 0.69. 1. (a) Write the equation of the regression line for predicting height. 2. (b) Interpret the slope and the intercept in this context. 3. (c) Calculate R2 of the regression line for predicting height from shoulder girth, and interpret it in the context of the application. 4. (d) A randomly selected student from your class has a shoulder girth of 100 cm. Predict the height of this student using the model. 5. (e) The student from part (d) is 160 cm tall. Calculate the residual, and explain what this residual means. 6. (f) A one year old has a shoulder girth of 56 cm. Would it be appropriate to use this linear model to predict the height of this child? *answers to 3 decimal points*!!!

Answer 1

7.20 Body measurements, Part III. Exercise 7.13 introduces data on shoulder girth and height of a group of individuals. The mean shoulder girth is 107.30 cm with a standard deviation of 10.34 cm. The mean height is 171.14 cm with a standard deviation of 9.41 cm. The correlation between height and shoulder girth is 0.69.

1. (a) Write the equation of the regression line for predicting height.

x: shoulder girth and y: height

The regression line is y=a+bx

slope= b= r*sy/sx = 0.69*9.41/10.34

=0.628

a =103.756

The regression line is

Height = 103.756+0.628* shoulder girth

2. (b) Interpret the slope and the intercept in this context.

When shoulder girth increases by 1 cm, the height increases by 0.628 cm.

It is not appropriate to interpret the intercept value because 0 value of shoulder girth is no meaning.

3. (c) Calculate R2 of the regression line for predicting height from shoulder girth, and interpret it in the context of the application.

R² =0.69*0.69 =0.4761

47.61% of variance in height is explained by shoulder girth.

4. (d) A randomly selected student from your class has a shoulder girth of 100 cm. Predict the height of this student using the model.

When shoulder girth=100 cm,

Predicted Height = 103.756+0.628* 100

= 166.556 cm

5. (e) The student from part (d) is 160 cm tall. Calculate the residual, and explain what this residual means.

Residual = 160-166.556 = -6.556

The negative residual means the student is over predicted by the model. ( the student have below average height).

6. (f) A one year old has a shoulder girth of 56 cm. Would it be appropriate to use this linear model to predict the height of this child? *answers to 3 decimal points*!!!

It is not appropriate to use this linear model to predict the height of this child because shoulder girth of 56 cm is not in the range of x values used to fit the model.