Worksheet 3 8/25/08
Problem 1. Children aged 3 to 8, who were randomly surveyed, were asked their ages and
were measured for height (in inches). Here is the data:
age height
3 36
3 38
4 37
4 40
5 39
6 42
6 45
7 40
8 46
(a) Make a scatterplot of these data
(b) Before calculating anything, describe the pattern of the data and decide if there is a
positive or negative association.
The pattern looks linear with a positive association.
(c) Calculate the correlation of the data.
r=.8201
(d) Calculate and plot the least-squares regression line for this data.
ˆy= 32.19 + 1.59x
(e) What is the residual for the observation (7,40)
y−ˆy= 40 −(32.19 + 1.59(7)) = 40 −43.32 = −3.32
(f) From this data, predict the height of a 50 year old. (is it wise to do so?)
ˆy= 32.19 + 1.59(50) = 111.69in
This seems unwise as extrapolation can yield some strange results.
