STA261 Assignment I
due: Wed.Feb.24/10
“How d’yuh like
them
apples!?”
Understanding the relationship between one experimental variable and an
other is often the main objective of a given study. Simply plotting a sample
of the joint outcomes for such variables may sometimes reveal an obvious
dependence of one on the other — linear, quadratic, or something perhaps
altogether fancier. But, to keep things simple, suppose that we have data
from two speciFc variables,
X
and
Y
, and that we wish to consider the
degree to which they may reasonably be understood to generate outcomes
that lie along a straight line of the general form
y
=
α
+
βx
:
±or example, it is generally thought that the percentage of apples attacked
by worms is greater on trees bearing a smaller crop.
Let
X
= size of crop (measures in basketsfull)
and
Y
= percentage of wormy fruit.
X
:8
,
6
,
11
,
22
,
14
,
17
,
18
,
24
,
19
,
23
,
26
,
40
Y
:
59
,
58
,
56
,
53
,
50
,
45
,
43
,
42
,
39
,
38
,
30
,
27
(1) Plot these data in the
x

y
plane. Of course, on doing so, one sees im
mediately the tendency of this particular sample of 12 points to fall
roughly along a straight line. But the basic ‘roughness’ of it is, in itself,