Exercise 7.15 introduces data on shoulder girth and height of a group of individuals. In the data set, the minimum shoulder girth is 87 cm and the maximum shoulder girth is 134 cm. The mean shoulder girth is 109.96 cm with a standard deviation of 10.18 cm. The mean height is 170.05 cm with a standard deviation of 9.38 cm. The correlation between height and shoulder girth is 0.687.
a) Write the equation of the regression line for predicting height.
Slope (round 3 decimal places): .612
Intercept (round to nearest whole number): 109
b) Interpret the slope in this context.
For each additional cm in height, the model predicts an additional b1 cm in shoulder girth
When height is 0 cm, the shoulder girth in cm is expected to be b1
For each additional cm in shoulder girth, the model predicts an additional b1 cm in height
When shoulder girth is 0 cm, the height in cm is expected to be b1
c) Calculate R^2 of the regression line for predicting height from shoulder girth. Round to three decimal places.
.477
Interpret R^2 in the context of the application.
About 100*(R^2)% of data in shoulder girth is accounted for by the model, i.e. explained by height
About 100*(R^2)% of the variability in height is accounted for by the model, i.e. explained by the shoulder girth
About 100*(R^2)% of the variability in shoulder girth is accounted for by the model, i.e. explained by the height
About 100*(R^2)% of the data in height is accounted for by the model, i.e. explained by the shoulder girth
d) A randomly selected student from your class has a shoulder girth of 103 cm. Predict the height of this student using the model. Round to the nearest whole number.
170
e) The student from part (d) is 164 cm tall. Calculate the residual and round to the nearest whole number.
-4
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?
Yes, this calculation would require interpolation.
Yes, this calculation would require extrapolation.
No, this calculation would require extrapolation.
No, this calculation would require interpolation.