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Homework answers / question archive / Refer to the data in MortgageRates3
Refer to the data in MortgageRates3.xlsx which contains average monthly 30-year mortgage rates (in %) over 82 consecutive months.
Use Solver to determine the weights for a four-period weighted moving average on the data set that minimizes the MSE.
(a)
What are the optimal values for the weights?
(w1, w2, w3, w4) =
(b)
Prepare a line graph comparing the weighted moving average predictions against the original data.
A chart with two line graphs has a horizontal axis labeled "Time Period" with values from 1 to 82 and a vertical axis labeled "Rate (in %)" with values from 6.1 to 8.6.
The line graph labeled "Rate" contains a series of 82 points connected by line segments. The points start at (1, 7.08), go generally up and right to reach a maximum at (16, 8.19), go generally down and right to reach a minimum at (34, 6.76), go generally up and right to reach a maximum at (53, 8.57), go generally down and right an end at (82, 6.16).
The line graph labeled "Forecast" contains a series of 78 points connected by line segments. The points start at (5, 7.47), and ends at (82, 6.43). This line graph appears to generally follow the same pattern as Rate but is shifted a few units right and is much smoother.
A chart with two line graphs has a horizontal axis labeled "Time Period" with values from 1 to 82 and a vertical axis labeled "Rate (in %)" with values from 6.1 to 8.6.
The line graph labeled "Rate" contains a series of 82 points connected by line segments. The points start at (1, 7.08), go generally up and right to reach a maximum at (16, 8.19), go generally down and right to reach a minimum at (34, 6.76), go generally up and right to reach a maximum at (53, 8.57), go generally down and right an end at (82, 6.16).
The line graph labeled "Forecast" contains a series of 78 points connected by line segments. The points start at (5, 7.08), and ends at (82, 6.7). This line graph appears to be the same as Rate but shifted 4 units right.
A chart with two line graphs has a horizontal axis labeled "Time Period" with values from 1 to 82 and a vertical axis labeled "Rate (in %)" with values from 6.1 to 8.6.
The line graph labeled "Rate" contains a series of 82 points connected by line segments. The points start at (1, 7.08), go generally up and right to reach a maximum at (16, 8.19), go generally down and right to reach a minimum at (34, 6.76), go generally up and right to reach a maximum at (53, 8.57), go generally down and right an end at (82, 6.16).
The line graph labeled "Forecast" contains a series of 81 points connected by line segments. The points start at (2, 7.08), and ends at (82, 6.27). This line graph appears to generally follow the same pattern as Rate but is shifted about 1 unit right and is much smoother.
A chart with two line graphs has a horizontal axis labeled "Time Period" with values from 1 to 82 and a vertical axis labeled "Rate (in %)" with values from 6.1 to 8.6.
The line graph labeled "Rate" contains a series of 82 points connected by line segments. The points start at (1, 7.08), go generally up and right to reach a maximum at (16, 8.19), go generally down and right to reach a minimum at (34, 6.76), go generally up and right to reach a maximum at (53, 8.57), go generally down and right an end at (82, 6.16).
The line graph labeled "Forecast" contains a series of 78 points connected by line segments. The points start at (5, 7.98), and ends at (82, 6.14). This line graph appears to be the same as Rate but shifted 1 unit right.
(c)
What are the forecasts (in %) for the next 2 months using this technique? (Round your answers to two decimal places.)
Month Period Forecast
11 83
%
12 84
%
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2.
[–/6 Points]
DETAILS
RAGSMDA9 11.E.008.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
The data set below contains annual sales (in $1,000s) for a small business.
Year Sales
1 284
2 289
3 335
4 389
5 405
6 411
7 415
8 436
9 427
10 436
11 463
12 451
13 473
14 475
15 498
16 486
17 522
18 529
19 533
20 551
Create an exponential smoothing model that minimizes the MSE for the data set. Use Solver to determine the optimal value of ?.
(a)
What is the optimal value of ??
? =
(b)
Prepare a line graph comparing the exponential smoothing predictions against the original data.
A chart with two line graphs has a horizontal axis labeled "Year" with values from 0 to 21 and a vertical axis labeled "Sales (in $1,000)" with values from 250 to 600.
The line labeled "Sales" contains a series of 20 points connected by line segments. The segments and the approximate points they connect are as follows. The segments start at (1, 284), go up and right through 7 points to (8, 436), go down and right to (9, 427), go up and right through 2 points to (11, 463), go down and right to (12, 451), go up and right through 3 points to (15, 498), go down and right to (16, 486), and go up and right through 4 points to stop at (20, 551).
The line labeled "Forecast" contains a series of 19 points connected by line segments. The segments and the approximate points they connect are as follows. The segments start at (2, 284), and go up and right through 18 points to stop at (20, 435).
A chart with two line graphs has a horizontal axis labeled "Year" with values from 0 to 21 and a vertical axis labeled "Sales (in $1,000)" with values from 250 to 600.
The line labeled "Sales" contains a series of 20 points connected by line segments. The segments and the approximate points they connect are as follows. The segments start at (1, 284), go up and right through 7 points to (8, 436), go down and right to (9, 427), go up and right through 2 points to (11, 463), go down and right to (12, 451), go up and right through 3 points to (15, 498), go down and right to (16, 486), and go up and right through 4 points to stop at (20, 551).
The line labeled "Forecast" contains a series of 19 points connected by line segments. The segments and the approximate points they connect are as follows. The segments start at (2, 284), go up and right through 7 points to (9, 436), go down and right to (10, 427), go up and right through 2 points to (12, 463), go down and right to (13, 451), go up and right through 3 points to (16, 498), go down and right to (17, 486), and go up and right through 3 points to stop at (20, 533).
A chart with two line graphs has a horizontal axis labeled "Year" with values from 0 to 21 and a vertical axis labeled "Sales (in $1,000)" with values from 250 to 600.
The line labeled "Sales" contains a series of 20 points connected by line segments. The segments and the approximate points they connect are as follows. The segments start at (1, 284), go up and right through 7 points to (8, 436), go down and right to (9, 427), go up and right through 2 points to (11, 463), go down and right to (12, 451), go up and right through 3 points to (15, 498), go down and right to (16, 486), and go up and right through 4 points to stop at (20, 551).
The line labeled "Forecast" contains a series of 19 points connected by line segments. The segments and the approximate points they connect are as follows. The segments start at (2, 287), go up and right through 7 points to (9, 432), go right to (10, 432), and go up and right through 10 points to stop at (20, 542).
A chart with two line graphs has a horizontal axis labeled "Year" with values from 0 to 21 and a vertical axis labeled "Sales (in $1,000)" with values from 250 to 600.
The line labeled "Sales" contains a series of 20 points connected by line segments. The segments and the approximate points they connect are as follows. The segments start at (1, 284), go up and right through 7 points to (8, 436), go down and right to (9, 427), go up and right through 2 points to (11, 463), go down and right to (12, 451), go up and right through 3 points to (15, 498), go down and right to (16, 486), and go up and right through 4 points to stop at (20, 551).
The line labeled "Forecast" contains a series of 19 points connected by line segments. The segments and the approximate points they connect are as follows. The segments start at (2, 287), go up and right through 4 points to (6, 450), go down and right through 2 points to (8, 421), go up and right to (9, 444), go down and right through 2 points to (11, 432), go up and right to (12, 477), go down and right to (13, 468), go up and right through 3 points to (16, 505), go down and right to (17, 500), go up and right through 2 points to (19, 558), and go down and right to stop at (20, 539).
(c)
What are the forecasts (in $1,000s) for the next 2 years using this technique?
Year Forecast
21 $
thousand
22 $
thousand
Need Help? Read It
3.
[–/6 Points]
DETAILS
RAGSMDA9 11.E.009.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
The data set below contains annual sales (in $1,000s) for a small business.
Year Sales
1 282
2 287
3 335
4 387
5 407
6 411
7 415
8 434
9 427
10 436
11 461
12 451
13 473
14 477
15 498
16 486
17 522
18 529
19 531
20 551
Use Holt's method to create a model that minimizes the MSE for the data set. Use Solver to determine the optimal values of ? and ?.
(a)
What are the optimal values of ? and ?? (Round your answers to four decimal places.)
? =
? =
(b)
Prepare a line graph comparing the predictions from Holt's method versus the original data.
A chart with two line graphs has a horizontal axis labeled "Year" with values from 0 to 21 and a vertical axis labeled "Sales (in $1,000)" with values from 250 to 600.
The line labeled "Sales" contains a series of 20 points connected by line segments. The segments and the approximate points they connect are as follows. The segments start at (1, 282), go up and right through 7 points to (8, 434), go down and right to (9, 427), go up and right through 2 points to (11, 461), go down and right to (12, 451), go up and right through 3 points to (15, 498), go down and right to (16, 486), and go up and right through 4 points to stop at (20, 551).
The line labeled "Forecast" contains a series of 19 points connected by line segments. The segments and the approximate points they connect are as follows. The segments start at (2, 282), go up and right through 7 points to (9, 446), go down and right to (10, 437), go up and right through 2 points to (12, 473), go down and right to (13, 460), go up and right through 3 points to (16, 509), go down and right to (17, 494), and go up and right through 3 points to stop at (20, 541).
A chart with two line graphs has a horizontal axis labeled "Year" with values from 0 to 21 and a vertical axis labeled "Sales (in $1,000)" with values from 250 to 600.
The line labeled "Sales" contains a series of 20 points connected by line segments. The segments and the approximate points they connect are as follows. The segments start at (1, 282), go up and right through 7 points to (8, 434), go down and right to (9, 427), go up and right through 2 points to (11, 461), go down and right to (12, 451), go up and right through 3 points to (15, 498), go down and right to (16, 486), and go up and right through 4 points to stop at (20, 551).
The line labeled "Forecast" contains a series of 19 points connected by line segments. The segments and the approximate points they connect are as follows. The segments start at (2, 282), go up and right through 7 points to (9, 434), go down and right to (10, 427), go up and right through 2 points to (12, 461), go down and right to (13, 451), go up and right through 3 points to (16, 498), go down and right to (17, 486), and go up and right through 3 points to stop at (20, 531).
A chart with two line graphs has a horizontal axis labeled "Year" with values from 0 to 21 and a vertical axis labeled "Sales (in $1,000)" with values from 250 to 600.
The line labeled "Sales" contains a series of 20 points connected by line segments. The segments and the approximate points they connect are as follows. The segments start at (1, 282), go up and right through 7 points to (8, 434), go down and right to (9, 427), go up and right through 2 points to (11, 461), go down and right to (12, 451), go up and right through 3 points to (15, 498), go down and right to (16, 486), and go up and right through 4 points to stop at (20, 551).
The line labeled "Forecast" contains a series of 19 points connected by line segments. The segments and the approximate points they connect are as follows. The segments start at (2, 285), go up and right through 4 points to (6, 451), go down and right through 2 points to (8, 419), go up and right to (9, 442), go down and right through 2 points to (11, 433), go up and right to (12, 474), go down and right to (13, 467), go up and right through 3 points to (16, 506), go down and right to (17, 499), go up and right through 2 points to (19, 558), and go down and right to stop at (20, 537).
A chart with two line graphs has a horizontal axis labeled "Year" with values from 0 to 21 and a vertical axis labeled "Sales (in $1,000)" with values from 250 to 600.
The line labeled "Sales" contains a series of 20 points connected by line segments. The segments and the approximate points they connect are as follows. The segments start at (1, 282), go up and right through 7 points to (8, 434), go down and right to (9, 427), go up and right through 2 points to (11, 461), go down and right to (12, 451), go up and right through 3 points to (15, 498), go down and right to (16, 486), and go up and right through 4 points to stop at (20, 551).
The line labeled "Forecast" contains a series of 19 points connected by line segments. The segments and the approximate points they connect are as follows. The segments start at (2, 285), and go up and right through 18 points to stop at (20, 541).
(c)
What are the forecasts (in $1,000s) for the next 2 years using this technique? (Round your answers to two decimal places.)
Year Forecast
21 $
thousand
22 $
thousand
Need Help? Read It
4.
[–/6 Points]
DETAILS
RAGSMDA9 11.E.010.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
The data set below contains annual sales (in $1,000s) for a small business.
Year Sales
1 284
2 287
3 337
4 389
5 405
6 411
7 417
8 434
9 427
10 436
11 461
12 453
13 475
14 475
15 496
16 486
17 524
18 527
19 533
20 551
Use regression analysis to fit a linear trend model to the data set.
(a)
What is the estimated regression function? (Use t for X1t where t = 1, 2, …. Round your numerical values to four decimal places.)
Y hatt =
(b)
Interpret the R2 value for your model. (Give your answer as a percent. Round your answer to one decimal place.)
Approximately
% of the
---Select---
accounted for by the model.
(c)
Prepare a line graph comparing the linear trend predictions against the original data.
A chart with two line graphs has a horizontal axis labeled "Year" with values from 0 to 21 and a vertical axis labeled "Sales (in $1,000)" with values from 250 to 600.
The line labeled "Sales" contains a series of 20 points connected by line segments. The segments and the approximate points they connect are as follows. The segments start at (1, 284), go up and right through 7 points to (8, 434), go down and right to (9, 427), go up and right through 2 points to (11, 461), go down and right to (12, 453), go up and right to (13, 475), go right to (14, 475), go up and right to (15, 496), go down and right to (16, 486), and go up and right through 4 points to stop at (20, 551).
The line labeled "Forecast" begins at the point (1, 284), goes up and right, and ends at the point (20, 551).
A chart with two line graphs has a horizontal axis labeled "Year" with values from 0 to 21 and a vertical axis labeled "Sales (in $1,000)" with values from 250 to 600.
The line labeled "Sales" contains a series of 20 points connected by line segments. The segments and the approximate points they connect are as follows. The segments start at (1, 284), go up and right through 7 points to (8, 434), go down and right to (9, 427), go up and right through 2 points to (11, 461), go down and right to (12, 453), go up and right to (13, 475), go right to (14, 475), go up and right to (15, 496), go down and right to (16, 486), and go up and right through 4 points to stop at (20, 551).
The line labeled "Forecast" begins at the point (1, 271), goes up and right, and ends at the point (20, 571).
A chart with two line graphs has a horizontal axis labeled "Year" with values from 0 to 21 and a vertical axis labeled "Sales (in $1,000)" with values from 250 to 600.
The line labeled "Sales" contains a series of 20 points connected by line segments. The segments and the approximate points they connect are as follows. The segments start at (1, 284), go up and right through 7 points to (8, 434), go down and right to (9, 427), go up and right through 2 points to (11, 461), go down and right to (12, 453), go up and right to (13, 475), go right to (14, 475), go up and right to (15, 496), go down and right to (16, 486), and go up and right through 4 points to stop at (20, 551).
The line labeled "Forecast" begins at the point (1, 324), goes up and right, and ends at the point (20, 556).
A chart with two line graphs has a horizontal axis labeled "Year" with values from 0 to 21 and a vertical axis labeled "Sales (in $1,000)" with values from 250 to 600.
The line labeled "Sales" contains a series of 20 points connected by line segments. The segments and the approximate points they connect are as follows. The segments start at (1, 284), go up and right through 7 points to (8, 434), go down and right to (9, 427), go up and right through 2 points to (11, 461), go down and right to (12, 453), go up and right to (13, 475), go right to (14, 475), go up and right to (15, 496), go down and right to (16, 486), and go up and right through 4 points to stop at (20, 551).
The line labeled "Forecast" begins at the point (1, 273), goes up and right, and ends at the point (20, 547).
(d)
What are the forecasts (in $1,000s) for the next 2 years using this technique? (Round your answers to two decimal places.)
Year Forecast
21 $
thousand
22 $
thousand
(e)
Fit a quadratic trend model to these data. What is the estimated regression function? (Use t for X1t and t2 for X2t where t = 1, 2, …. Round your numerical values to four decimal places.)
Y hatt =
(f)
Compare the adjusted-R2 value for this model to that of the linear trend model. What is implied by this comparison? (Round your answers to four decimal place.)
The adjusted-R2 value for the quadratic model is
. The adjusted-R2 value for the linear model is
. These results
---Select---
suggest that the quadratic model is an improvement over the linear model.
(g)
Prepare a line graph comparing the quadratic trend predictions against the original data.
A chart with two line graphs has a horizontal axis labeled "Year" with values from 0 to 21 and a vertical axis labeled "Sales (in $1,000)" with values from 250 to 600.
The line labeled "Sales" contains a series of 20 points connected by line segments. The segments and the approximate points they connect are as follows. The segments start at (1, 284), go up and right through 7 points to (8, 434), go down and right to (9, 427), go up and right through 2 points to (11, 461), go down and right to (12, 453), go up and right to (13, 475), go right to (14, 475), go up and right to (15, 496), go down and right to (16, 486), and go up and right through 4 points to stop at (20, 551).
The curve labeled "Forecast" begins at the point (1, 284), goes up and right becoming less steep, and ends at the point (20, 533).
A chart with two line graphs has a horizontal axis labeled "Year" with values from 0 to 21 and a vertical axis labeled "Sales (in $1,000)" with values from 250 to 600.
The line labeled "Sales" contains a series of 20 points connected by line segments. The segments and the approximate points they connect are as follows. The segments start at (1, 284), go up and right through 7 points to (8, 434), go down and right to (9, 427), go up and right through 2 points to (11, 461), go down and right to (12, 453), go up and right to (13, 475), go right to (14, 475), go up and right to (15, 496), go down and right to (16, 486), and go up and right through 4 points to stop at (20, 551).
The curve labeled "Forecast" begins at the point (1, 284), goes up and right becoming less steep, and ends at the point (20, 551).
A chart with two line graphs has a horizontal axis labeled "Year" with values from 0 to 21 and a vertical axis labeled "Sales (in $1,000)" with values from 250 to 600.
The line labeled "Sales" contains a series of 20 points connected by line segments. The segments and the approximate points they connect are as follows. The segments start at (1, 284), go up and right through 7 points to (8, 434), go down and right to (9, 427), go up and right through 2 points to (11, 461), go down and right to (12, 453), go up and right to (13, 475), go right to (14, 475), go up and right to (15, 496), go down and right to (16, 486), and go up and right through 4 points to stop at (20, 551).
The curve labeled "Forecast" begins at the point (1, 302), goes up and right becoming less steep, and ends at the point (20, 534).
A chart with two line graphs has a horizontal axis labeled "Year" with values from 0 to 21 and a vertical axis labeled "Sales (in $1,000)" with values from 250 to 600.
The line labeled "Sales" contains a series of 20 points connected by line segments. The segments and the approximate points they connect are as follows. The segments start at (1, 284), go up and right through 7 points to (8, 434), go down and right to (9, 427), go up and right through 2 points to (11, 461), go down and right to (12, 453), go up and right to (13, 475), go right to (14, 475), go up and right to (15, 496), go down and right to (16, 486), and go up and right through 4 points to stop at (20, 551).
The curve labeled "Forecast" begins at the point (1, 259), goes up and right becoming less steep, and ends at the point (20, 551).
(h)
What are the forecasts (in $1,000s) for the next 2 years using this technique? (Round your answers to two decimal places.)
Year Forecast
21 $
thousand
22 $
thousand
(i)
If you had to choose between the linear and quadratic trend models, which would you use? Why?
