The regression relationship for y = student height and x = father's height for the 10 female students listed in the table for Exercise 3.12 and in the dataset UCDchap3 is
y^ = 19.42 + 0.658x
a. Give the value of the y-intercept. Does it have a meaningful interpretation in this situation? Explain.
b. Give the value of the slope and interpret what it means in this situation.
c. Use the equation to predict the height of a female student whose father is 70 inches tall.
d. One student was 67 inches tall and her father was 70 inches tall. Find the residual for this student and explain what it tells you about this student in relation to other female students whose fathers are 70 inches tall.
e. Would it make sense to use this regression equation to predict the height of a male student whose father is 70 inches tall? Explain.
Exercise
The following table shows sex, height (inches), and midparent height (inches) for a sample of 18 college students. The variable mid-parent height is the average of mother's height and father's height. (These data are in the dataset UCDchap3 on the companion website; they are sampled from the larger dataset UCDavis2.)
|
Sex, Height and Mid-Parent Height for 18 college students
|
|
Sex
|
Height
|
Mid-Parent Height
|
|
M
|
71
|
64.0
|
|
F
|
60
|
63.5
|
|
F
|
66
|
67.0
|
|
M
|
70
|
64.5
|
|
F
|
65
|
65.5
|
|
F
|
66
|
69.5
|
|
M
|
74
|
72.5
|
|
F
|
67
|
67.5
|
|
F
|
63
|
65.5
|
|
M
|
67
|
64.0
|
|
F
|
69
|
70.0
|
|
M
|
65
|
63.0
|
|
M
|
72
|
69.0
|
|
M
|
68
|
67.0
|
|
F
|
63
|
63.0
|
|
F
|
61
|
63.0
|
|
M
|
74
|
69.5
|
|
F
|
65
|
67.5
|
a. In the relationship between height and mid-parent height, which variable is the response variable (y) and which is the explanatory variable (x)?
b. Draw a scatterplot of the data for the y and x variables defined in part (a). Use different symbols for males and females.
c. Briefly interpret the scatterplot. Does the association appear to be linear? What are the differences between the males and females? Which points, if any, are outliers?
d. Calculate the difference between height and mid-parent height for each student, and draw a scatterplot of y = difference versus x = mid-parent height. Use different symbols for males and females. What does this graph reveal about the connection between height and midparent height?