Question
In: Statistics and Probability
23-64) Let Yt be the sales during month t (in thousands of dollars) for a photography...
23-64) Let Yt be the sales during
month t (in thousands of dollars) for a photography
studio, and let Pt be the price charged for portraits
during month t. The data are in the file Week 4 Assignment
Chapter 12 Problem 64. Use regression to fit the following model to
these data:
Yt = a + b1Yt−1 + b2Pt + et
This equation indicates that last month’s sales and the current
month’s price are explanatory variables. The last term, et, is an
error term. Show all work.
- If the price of a portrait during month 21 is $10, what would you predict for sales in month 21?
- Does there appear to be a problem with autocorrelation of the residual? Explain your answer
Data:
| Sales | Price |
| $400,000 | $15 |
| $1,042,000 | $12 |
| $1,129,000 | $24 |
| $1,110,000 | $18 |
| $1,336,000 | $18 |
| $1,363,000 | $30 |
| $1,177,000 | $27 |
| $603,000 | $24 |
| $582,000 | $36 |
| $697,000 | $27 |
| $586,000 | $24 |
| $673,000 | $27 |
| $546,000 | $30 |
| $334,000 | $33 |
| $27,000 | $24 |
| $76,000 | $27 |
| $298,000 | $30 |
| $746,000 | $18 |
| $962,000 | $21 |
| $907,000 | $24 |
Solutions
Expert Solution
Regression Analysis: Sales versus Sales(t-1), Price
The
regression equation is
Sales = 589667 + 0.741 Sales(t-1) - 16124 Price
Predictor Coef SE Coef T P
Constant 589667 268264 2.20 0.042
Sales(t-1) 0.7412 0.1486 4.99 0.000
Price -16124 9506 -1.70 0.108
S = 252212 R-Sq = 63.0% R-Sq(adj) = 58.7%
If the price of a portrait during month 21 is $10, what would you predict for sales in month 21?
Does there appear to be a problem with autocorrelation of the residual? Explain your answer.
Ans: The price of a portrait during month 21 is $10, then the predict for sales in month 21
Sales = 589667 + 0.741 *907,000 - 16124 *10 = $1141269.
There is no autocorrelation between the error. Hence, there is no problem.
| Sales(Y(t)) | Sales(Y(t-1)) | Price |
| $400,000 | mean(Y(t)) | $15 |
| $1,042,000 | $400,000 | $12 |
| $1,129,000 | $1,042,000 | $24 |
| $1,110,000 | $1,129,000 | $18 |
| $1,336,000 | $1,110,000 | $18 |
| $1,363,000 | $1,336,000 | $30 |
| $1,177,000 | $1,363,000 | $27 |
| $603,000 | $1,177,000 | $24 |
| $582,000 | $603,000 | $36 |
| $697,000 | $582,000 | $27 |
| $586,000 | $697,000 | $24 |
| $673,000 | $586,000 | $27 |
| $546,000 | $673,000 | $30 |
| $334,000 | $546,000 | $33 |
| $27,000 | $334,000 | $24 |
| $76,000 | $27,000 | $27 |
| $298,000 | $76,000 | $30 |
| $746,000 | $298,000 | $18 |
| $962,000 | $746,000 | $21 |
| $907,000 | $962,000 | $24 |
In excell,
1. Select "Data".
2. Select " Data Analysis"
3. Select "Regression"
4. Put Y(t) at "Input Y range.
5. Put Y(t-1) and Price at "Input X range".
6. Click OK
orchestra answered 2 years agoRelated Solutions
Let x be per capita income in thousands of dollars. Let y be the number of...
Let x be per capita income in thousands of dollars. Let y be the
number of medical doctors per 10,000 residents. Six small cities in
Oregon gave the following information about x and y. x 8.6 9.7 10.3
8.0 8.3 8.7 y 9.7 19.0 22.0 10.2 11.4 13.1 Complete parts (a)
through (e), given Σx = 53.6, Σy = 85.4, Σx2 = 482.72, Σy2 =
1344.7, Σxy = 784.51, and r ≈ 0.963.
(b) Verify the given sums Σx, Σy,...
Let x be per capita income in thousands of dollars. Let y be the number of...
Let x be per capita income in thousands of dollars. Let
y be the number of medical doctors per 10,000 residents.
Six small cities in Oregon gave the following information about
x and y.
x
9.0
9.4
10.2
8.0
8.3
8.7
y
9.5
18.0
21.2
10.2
11.4
13.1
Complete parts (a) through (e), given Σx = 53.6,
Σy = 83.4, Σx2 = 481.98,
Σy2 = 1269.3, Σxy = 761.13, and
r ≈ 0.864.
(b) Verify the given sums Σx, Σy,...
Let x be per capita income in thousands of dollars. Let y be the number of...
Let x be per capita income in thousands of dollars. Let y be the
number of medical doctors per 10,000 residents. Six small cities in
Oregon gave the following information about x and y. x 8.4 9.1 9.8
8.0 8.3 8.7 y 9.8 18.4 21.2 10.2 11.4 13.1 Complete parts (a)
through (e), given Σx = 52.3, Σy = 84.1, Σx2 = 457.99, Σy2 =
1289.65, Σxy = 747.71, and r ≈ 0.958. (a) Draw a scatter diagram
displaying the...
Let x be per capita income in thousands of dollars. Let y be the number of...
Let x be per capita income in thousands of dollars. Let y be the
number of medical doctors per 10,000 residents. Six small cities in
Oregon gave the following information about x and y. x 8.3 9.3 10.2
8.0 8.3 8.7 y 9.9 18.1 20.6 10.2 11.4 13.1 Complete parts (a)
through (e), given Σx = 52.8, Σy = 83.3, Σx2 = 468, Σy2 = 1255.59,
Σxy = 750.81, and r ≈ 0.974. (a) Draw a scatter diagram displaying
the...
3.4- Let Y1 = θ0 + ε1 and then for t > 1 define Yt recursively...
3.4- Let Y1 = θ0 + ε1 and then for t > 1 define Yt recursively
by Yt = θ0 + Yt−1 + εt. Here θ0 is a constant. The process {Yt} is
called a random walk with drift.
(c) Find the autocovariance function for {Yt}.
An airline manufacturer incurred the following costs last month (in thousands of dollars):
An airline manufacturer incurred the following costs last month (in thousands of dollars):
Requirement 1. Assuming the cost object is an airplane, classify each cost as one of the following: direct material (DM), direct labor (DL), indirect labor (IL), indirect materials (IM), other manufacturing overhead (other MOH), or period cost. What is the total for each type of cost? (Enter currency amounts in thousands and not in dollars. If a box is not used in the table leave the box...
the following are the monthly sales (in thousands of dollars) for a company in four regions...
the following are the monthly sales (in thousands of dollars)
for a company in four regions of the country.
North
East
South
West
34
28
18
24
47
36
30
38
44
40
30
41
29
21
30
24
37
23
Does the data suggest that there is a difference in the mean
monthly sales among the different regions?
The chart below lists the sales in thousands of dollars based on the advertising budget for...
The chart below lists the sales in thousands of dollars based on
the advertising budget for that quarter. The regression equation is
Y' = 4.073 + 0.8351X. What is the correlation
coefficient?
Advertising ($hunderds)
Sales ($thousands)
0
5
3
5.5
4
7
5
7.8
6
9
7
11
Multiple Choice
0.775
0.844
0.926
1.00
Let x represent the average annual salary of college and university professors (in thousands of dollars)...
Let x represent the average annual salary of college
and university professors (in thousands of dollars) in the United
States. For all colleges and universities in the United States, the
population variance of x is approximately
σ2 = 47.1. However, a random sample of 18
colleges and universities in Kansas showed that x has a
sample variance s2 = 80.5. Use a 5% level of
significance to test the claim that the variance for colleges and
universities in Kansas is...
Let x represent the average annual salary of college and university professors (in thousands of dollars)...
Let x represent the average annual salary of college
and university professors (in thousands of dollars) in the United
States. For all colleges and universities in the United States, the
population variance of x is approximately
σ2 = 47.1. However, a random sample of 14
colleges and universities in Kansas showed that x has a
sample variance s2 = 82.6. Use a 5% level of
significance to test the claim that the variance for colleges and
universities in Kansas is...
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
- Charming Paper Company sells to the 12 accounts listed here. Account Receivable Balance Outstanding Average...
- Computer Networks IT 210 Please Use your own words . sorry No handwriting no copy paste...
- I would like to integrate a bubble sort into this binary search in c ++ Thank...
- Answer the bottom in 1-2 paragraphs Classical conditioning is a learned behavior where previously neutral response...
- identify one intrapersonal relationship and evaluate its component.
- Using Python in vs code: The distribution of letters in a document has a distinctive and...
- Why is De Beers exploring the diamond reselling market? How does the creation of IIDV affect...
ADVERTISEMENT