A contractor developed a multiplicative time-series model to forecast the number of contracts in future quarters, using quarterl
1 answer:
There is a missing content in the question.
After the statements and before the the options given; there is an omitted content which says:
Referring to Table 16-5, in testing the coefficient of X in the regression equation (0.117) the results were a t-statistic of 9.08 and an associated p-value of 0.0000. Which of the following is the best interpretation of this result?
Answer:
C. The quarterly growth rate in the number of contracts is significantly different from 0% (? = 0.05).
Step-by-step explanation:
From the given question:
The resulting regression equation can be represented as:
where;
the estimated number of contracts in a quarter X is the coded quarterly value with X = 0
the first quarter of 2010 Q1 is a dummy variable equal to 1 in the first quarter of a year and 0 otherwise
Q2 is a dummy variable equal to 1 in the second quarter of a year and 0 otherwise
Q3 is a dummy variable equal to 1 in the third quarter of a year and 0 otherwise
Our null and alternative hypothesis can be stated as;
Null hypothesis :
The quarterly growth rate in the number of contracts is not significantly different from 0% (? = 0.05)
The quarterly growth rate in the number of contracts is significantly different from 0% (? = 0.05)
The decision rule is to reject the null hypothesis if the p-value is less than 0.05.
From the missing omitted part we added above; we can see that the t-statistics value = 9.08 and the p-value = 0.000 .
Conclusion:
Thus; we reject the null hypothesis and accept the alternative hypothesis. i.e
The quarterly growth rate in the number of contracts is significantly different from 0% (? = 0.05)
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Answer:
<h2>See the explanation.</h2>Step-by-step explanation:
(a)
= A.
In the above matrix A, the columns refers the three type of books and the rows refers the from which stores the books are been sold.
The numbers represents the corresponding sales in the month of January.
The sale is same for the 6 months.
Hence, 6A = . This matrix 6A represents the total sales over the 6 months.
(b)
If we denote the books in stock at the starting of January by B, then
B = .
Each month, the chain restocked the stores from its warehouse by shipping 500 hardcover, 1,400 softcover, and 1,400 plastic books to San Francisco and 500 hardcover, 500 softcover, and 500 plastic books to Los Angeles.
If we represent the amount restocked books at the end of each month by another matrix C, then
C = .
This restocking will be done for 5 times before the end of June.
If there would be no sale, then the stock would be
B + 5C = .
Since, the total sale is given by 6A, at the end of June, the inventory in each store can be shown as following,
B+5C-6A
The rows add up to
The sum of the numbers in row
The last problem can be solved with the binomial theorem, but I'll assume you don't take that for granted. You can prove this claim by induction. When
so the base case holds. Assume the claim holds for
Use this to show that it holds for
Notice that
So you can write the expansion for
and since
and so the claim holds for
Setting
which agrees with the result obtained for part (c).