# Develop a multiple regression model of the form

Question

Question 24

Develop a multiple regression model of the form

using the following data to predict y from x. From a scatter plot and Tukey’s ladder of transformation, explore ways to

recode the data and develop an alternative regression model. Compare the results.

Appendix A Statistical Tables

y

2,485

1,790

874

2,190

3,610

2,847

1,350

x

3.87

3.22

2.91

3.42

3.55

3.61

3.13

y

740

4,010

3,629

8,010

7,047

5,680

1,740

x

2.83

3.62

3.52

3.92

3.86

3.75

3.19

(Round your answers to 4 decimal places.)

logy =

+

x

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Question 25

Study the output given here from a stepwise multiple regression analysis to predict y from four variables. Comment

on the output at each step.

Appendix A Statistical Tables

Number of steps =

(Round the coefficients 1,2,3,4 to 2 decimal places, round the coefficient 5 to 4 decimal places.)

Regression model at the last step:

+

+

+

+

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Question 26

The “Economic Report to the President of the United States” included data on the amounts of

manufacturers? new and unfilled orders in millions of dollars. Shown here are the figures for new

orders over a 21-year period. Use a computer to develop a regression model to fit the trend effects

for these data. Use a linear model and then try a quadratic model. How well does either model fit

the data?

Year

Total Number of New Orders

1

2

3

4

5

6

7

8

9

10

55,022

55,921

64,182

76,003

87,327

85,139

99,513

115,109

131,629

147,604

11

156,359

Year

*(Round your answers to the nearest integer.)

**(Round your answer to 1 decimal place.)

?=

*+(

*) Period

?=

*+(

*) Period + (

**) Period2

12

13

14

15

16

17

18

19

20

21

Total Number of New Orders

168,025

162,140

175,451

192,879

195,706

195,204

209,389

227,025

240,758

243,643

The

regression trend model is superior, the period2 variable

a significant addition to the model.

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Question 27

Current Construction Reports from the U.S. Census Bureau contain data on new privately owned housing units. Data

on new privately owned housing units (1000s) built in the West between 1980 and 2010 follow. Use these time-series

data to develop an autoregression model with a one-period lag. Now try an autoregression model with a two-period

lag. Discuss the results and compare the two models.

Year

Housing Starts (1000)

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

318.9

251.3

224.1

390.4

457.3

483.9

509.7

406.0

415.6

402.1

324.9

247.9

268.6

288.2

342.4

1995

328.5

Year

Housing Starts (1000)

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

347.4

363.5

401.2

404.3

401.5

413.0

430.9

486.5

541.9

558.6

455.2

343.9

196.7

116.7

128.3

*(Round your answer to 1 decimal places.)

**(Round your answer to 2 decimal places.)

***(Round your answer to 3 decimal place.)

****(Round your answer to the nearest integer.)

The model with a 1 – period lag:

Housing Starts =

*+

** lag 1

F=

** p =

*** R2 =

*% adjusted R2 =

*% se =

**

The model with 2 – period lag:

Housing Starts =

**** +

** lag 2

F=

** p =

*** R2 =

*% adjusted R2 =

*% se =

**

The model with

is better model with a

R2. The model with

is

.

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Question 28

The following data contain the quantity (million pounds) of U.S. domestic fish caught annually over a 25-year period

as published by the National Oceanic and Atmospheric Administration.

a. Use a 3-year moving average to forecast the quantity of fish for the years 1989 through 2010 for these data.

Compute the error of each forecast and then determine the mean absolute deviation of error for the forecast.

b. Use exponential smoothing and to forecast the data from 1989 through 2010. Let the forecast for 1987 equal the

actual value for 1986. Compute the error of each forecast and then determine the mean absolute deviation of error for

the forecast.

c. Compare the results obtained in parts (a) and (b) using MAD. Which technique seems to perform better? Why?

Year

Quantity

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

6,137

7,019

7,391

8,750

9,816

9,644

9,951

9,971

10,089

9,693

9,380

1997

9,615

1998

8,992

1999

9,089

Year

Quantity

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

8,876

9,290

9,250

9,315

9,424

9,379

9,180

9,026

7,953

7,875

7,994

(Round your answers to 2 decimal place.)

a. MADmoving average :

b. MAD? = .2 :

c. The

produced a smaller MAD than did

. Using MAD as the criterion,

was a better forecasting tool than the

.

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