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STP 226
STP 226
ELEMENTARY STATISTICS
CHAPTER 4
DESCRIPTIVE MEASURES IN REGRESSION AND CORRELATION
Linear Regression
and
correlation
allows us to examine the relationship between two or
more quantitative variables.
4.1
Linear Equations with one Independent Variable
y = b
0
+ b
1
x
is a straight line where b
0
and b
1
are constants,
b
0
is the
yintercept
( value of y for x=0) and b
1
is the
slope
of the line.
Slope (b
1
) represents change in y for corresponding change in x, for every 1 unit increase
in x value there is a b
1
unit vertical increase/decrease in y value , depending on the line.
The straightline graph of the linear equation y = b
0
+ b
1
x slopes upward if b
1
> 0, slopes
downward if b
1
< 0, and is horizontal if b
1
= 0.
Note: on the picture b
0
=
β
0
, b
1
=β
1
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STP 226
4.2
The Regression Equation
Often, in real life situations, it is not likely to have data that follow some straight line
perfectly.
A
scatterplot (scatter diagram)
is useful in visualizing apparent relationships between
two variables x and y
y
– response variable
or dependent variable
x – predictor variable/explanatory variable or independent variable
Example(Table 4.2)
(Age and price of a Orion)
Car (Orion)
1
2
3
4
5
6
7
8
9
10
11
Age (yr):
x
5
4
6
5
5
5
6
6
2
7
7
Price ($100):
y
85
103
70
82
89
98
66
95
169
70
48
If the points seem to follow a straight line, then a straight line can be used to approximate
the relationship. Scatter plot above shows relatively strong positive linear trend.
Sometimes the plot may show another type of the relationship , like quadratic or
exponential.
Fitting the line to the data that shows no linear trend or other than linear trend is not
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 Spring '09
 VINH

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