# Develop a multiple regression model of the form

March 14, 2016

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

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

?=
*+(
*) 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

The model with a 1 – period lag:
Housing Starts =
*+
** lag 1
F=

** p =
*** R2 =
*% se =
**
The model with 2 – period lag:
Housing Starts =
**** +
** lag 2
F=
** p =
*** 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
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