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STATS 60, Spring 2008
April 9, Lecture 06
1
Slope and intercept
Soon we will begin our discussion on regression, and in regression we will want to draw a straight line through
a group of points. To get ready, let’s review the equation of a line. Our example data is listed in Table 1. A
plot of the data is shown in Figure 1
You will recognize the equation for this conversion, of course. It is
C
=
5
9
(
F

32)
. Now, the classic equation
for a line is
y
=
mx
+
b
, where the slope is
m
and the
y
intercept is
b
. Are these two equations the same?
To ﬁnd out, substitute the symbols
y
for
C
and
x
for
F
. Then we have
y
=
5
9
(
x

32)
. Next, multiply
everything in the parenthesis by
5
9
. We get
y
= 0
.
56
x

17
.
8
, or
y
=
mx
+
b
with
m
= 0
.
56
and
b
=

17
.
8
.
The slope is the "rise/run" or "(change in
y
)/(change in
x
)", so in this case for every degree increase in
F
there is an 0.56 degree increase in
C
. From the (positive) value of
m
(as well as from the ﬁgure) we know
that as
x
increases, so does
y
. If the slope were negative,
y
would decrease as
x
increases.
Notice that there is no statistics involved with the equation
y
=
mx
+
b
. If you know
x
exactly, you know
y
exactly. No probability comes into play. Not only is there no uncertainty involved, we have more data then
we need. The equation for a line has two unknowns,
m
and
b
. To determine them we only need two data
points.
After reading Chapter 7 you should be comfortable with the following:
•
locating points on a graph given an (
x, y
) coordinate
•
ﬁnding a slope and intercept given two points
•
determining if a second point is on a line given a slope and a point
•
determining if a point is on a line given a slope and an intercept
•
identifying a line with a positive, zero, and negative slope
Deg F, (
x
)
Deg C, (
y
)
100
37.8
64
17.8
71
21.7
Table 1. Conversion to degrees C from degrees F
1
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View Full DocumentFigure 1. Conversion of degrees F to degrees C
Scatter plots
Now consider a problem where you collect a good amount of data for two variables, which may or may not
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 Spring '08
 Boik,J

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