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:
2. Test the overall significance of the model:
(1) What are H0 and Ha
(2) What are the F value and the F critical value
(3) Reject or do not reject H0
(4) Is the model significant?
3. Test the significance of the linear trend (t):
(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 the linear trend significant?
4. Test the significance of Q2:
(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?
5. Test the significance of Q3:
(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 Q3 significant?
6. Test the significance of Q4:
(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 Q4 significant?