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
This preview has intentionally blurred sections. Sign up to view the full version.
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
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 Boik,J
 Addition, Variance, Pearson productmoment correlation coefficient, Covariance and correlation, Freedman

Click to edit the document details