The Standard Deviation of the
Regression Slope
•
The standard error of the regression slope
coefficient (b
1
) is estimated by
n
x)
(
x
s
)
x
(x
s
s
2
2
ε
2
ε
b
1
where:
= Estimate of the standard error of the least squares slope
= Sample standard error of the estimate
1
b
s
2
n
SSE
s
ε

Inference about the Slope:
t Test
•
t test for a population slope
–
Is there a linear relationship between x and y?
•
Null and alternative hypotheses
–
H
0
:
β
1
= 0
(no linear relationship)
–
H
1
:
β
1
0
(linear relationship does exist)
•
Test statistic
–
–
1
b
1
1
s
β
b
t
2
n
d.f.
where:
b
1
= Sample regression slope
coefficient
β
1
= Hypothesized slope
s
b1
= Estimator of the standard
error of the slope