CHAPTER 13 Simple Linear Regression

540 CHAPTER THIRTEEN Simple Linear Regression
FIGURE 13.17
Microsoft Excel t test
for the slope for the
Sunflowers Apparel data
From Figure 13.17,
See Section E13.1 to create
the worksheet that contains
this area.
and
b 1 =+ 1. 6699 n = 14 S b = 0.
1569
1
t
b1 − β1
=
S b 1
1.
6699 − 0
=
0.
1569
= 10.
6411
Microsoft Excel labels this t statistic t Stat (see Figure 13.17). Using the 0.05 level of significance,
the critical value of t with n − 2 = 12 degrees of freedom is 2.1788. Because t = 10.6411 >
2.1788, you reject H 0
(see Figure 13.18). Using the p-value, you reject H 0
because the p-value
is approximately 0 which is less than α = 0.05. Hence, you can conclude that there is a significant
linear relationship between mean annual sales and the size of the store.
FIGURE 13.18
Testing a hypothesis
about the population
slope at the 0.05 level
of significance, with
12 degrees of freedom
–2.1788 0 +2.1788 t 12
Region of
Rejection
Region of
Nonrejection
Region of
Rejection
Critical
Value
Critical
Value
F Test for the Slope
As an alternative to the t test, you can use an F test to determine whether the slope in simple
linear regression is statistically significant. In Section 10.4, you used the F distribution to test
the ratio of two variances. Equation (13.17) defines the F test for the slope as the ratio of the
2
variance that is due to the regression (MSR) divided by the error variance (MSE = ).
S YX
TESTING A HYPOTHESIS FOR A POPULATION SLOPE, β 1
, USING THE F TEST
The F statistic is equal to the regression mean square (MSR) divided by the error mean
square (MSE).
F
=
MSR
MSE
(13.17)