Consider the following set of quarterly sales (y) data, given in
thousands of dollars.
year
quarter
y
t
1
winter
1690
1
spring
940
2
summer
2625
3
fall
2500
4
2
winter
1800
5
spring
900
6
summer
2900
7
fall
2360
8
3
winter
1850
9
spring
1100
10
summer
2390
11
fall
2615
12
The following dummy variable model that incorporates a linear trend
and constant seasonal variation was used: y(t) =
B0 + B1t +
BQ2(Q2) +
BQ3(Q3) +
BQ4(Q4) + Et. In
this model, there are 3 binary seasonal variables (Q2,
Q3, and Q4), where Qi is a binary (0,1)
variable defined as:
Q2 = 1, if the time
series data is associated with spring quarter;
Q2 = 0, if the time
series data is not associated with spring quarter.
Q3 = 1, if the time series data
is associated with summer quarter;
Q3 = 0, if the time series data
is not associated with summer quarter.
Q4 = 1, if the time series data
is associated with fall quarter;
Q4 = 0, if the time series data
is not associated with fall quarter.
At α = .05, use Excel to run the regression and answer
the following questions:
4. Test the significance of Q2 (4 points):
(1) What are H0 and Ha
(2) What are the t value and the
t critical values
(3) Reject or do not reject H0
(4) Is Q2 significant?