CHAPTER 2
Exercise Solutions
Exercise 2.1
(a)
y
342424
221100
130010
−11−24−12
00−11−22
=
51001008
(b)
is the estimated slope of the fitted line.
is the estimated value of when ; it is the intercept of the fitted line.
(c)
(d)
343.60.40.161.2
222.8−0.80.64−1.6
132111
-110.40.60.36−0.6
001.2−1.21.440
= = = = = =
5101003.60
Exercise 2.1 (continued)
(e)
Figure xr2.1 Observations and fitted line
(f) See figure above. The fitted line passes through the point of the means, .
(g) Given , , , and , we have
(h)
(i)
(j) and
Exercise 2.2
(a)
Figure xr2.2(a) Sketch of solution
(b)
Figure xr2.2(b) Sketch of solution
Exercise 2.2 (continued)
(c)
(d)
Exercise 2.3
(a) The observations on y and x and the estimated least-squares line are graphed in part (b). The line drawn for part (a) will depend on each student’s subjective choice about the position of the line. We show the least squares fitted line.
Figure xr2.3(a) Observations and line through data
(b) Preliminary calculations yield:
The least squares estimates are:
Figure xr2.3(b) Observations and fitted line
Exercise 2.3 (continued)
(c) and
The predicted value for y at is