NAME
STAT 269 - Introductory Statistics
Brief Summary of Regression and Correlation
General model:
y
=
0
+
1
x
+
"
Summary values we will use:
S
xx
=
P
(
x
x
)
2
n
S
yy
=
P
(
y
y
)
2
n
S
xy
=
P
((
x
x
)(
y
y
))
n
From these we can get our estimates:
^
1
=
b
1
=
S
xy
S
xx
^
0
=
b
0
=
y
b
1
x
To calculate the correlation between the variables:
r
=
S
xy
p
S
xx
S
yy
Interpreting the correlation:
1
< r <
:
9 implies a strong negative correlation
:
9
< r <
:
5 implies a moderate negative correlation
:
5
< r <
0 implies a weak negative correlation
0
< r < :
5 implies a weak positive correlation
:
5
< r < :
9 implies a moderate positive correlation
:
9
< r <
1 implies a strong positive correlation
Summary of the Hypothesis testing:
1.
Hypotheses:
H
0
:
1
= 0
H
a
:
1
6
= 0
Where:
1
is the slope in our regression model
2.
Assumptions:
We are assuming that our simple linear regression model,
y
=
0
+
1
x
+
"
,
describes the relationship between the two factors, and that the errors,
"
, come randomly from a
population that follows a normal distribution with mean zero.
.
.
.
6.
Conclusion:
State it in terms of the problem.