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Question 34 Determine the Pearson product-moment correlation
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Question 34

Determine the Pearson product-moment correlation coefficient for the following data.

x

1

10

9

7

4

3

2

y

8

4

6

5

7

7

9


(Do not round the intermediate values. Round your answer to 3 decimal places.)


Correlation coefficient, r =

Question 35

Country

Per Capita
Personal
Consumption
($ U.S.)

Paper
Consumption
(kg per person)

Fish
Consumption
(lbs per person)

Gasoline
Consumption
(liters per person)

Bangladesh

836

1

23

2

Greece

3,145

85

53

394

Italy

21,785

204

48

368

Japan

37,931

250

141

447

Kenya

276

4

12

16

Norway

1,913

156

113

477

Philippines

2,195

19

65

43

Portugal

3,154

116

133

257

United Kingdom

19,539

207

44

460

United States

109,521

308

47

1,624

Venezuela

622

27

40

528



(Round your answers to 4 decimal places.)

The regression equation is: Per Capita =

+ (

) Paper Consumption + (

) Fish Consumption + (

) Gasoline Consumption

This model yields an F =

with p-value =

. Thus, there is overall significance at ? = .01. One of the three predictors is significant. Gasoline Consumption has a t = 2.67 with p-value of

which is statistically significant at ? = .05. The p-values of the t statistics for the other two predictors are insignificant indicating that a model with just Gasoline Consumption as a single predictor

nearly as strong.

Question 36

Dun & Bradstreet reports, among other things, information about new business incorporations and number of business failures over several years. Shown here are data on business failures and current liabilities of the failing companies over several years. Use these data and the following model to predict current liabilities of the failing companies by the number of business failures. Discuss the strength of the model.



Now develop a different regression model by recoding x. Use Tukey's four-quadrant approach as a resource. Compare your models.

Rate of Business
Failures
(10,000)

Current Liabilities
of Failing Companies
($ millions)

44

1,888

43

4,380

42

4,635

61

6,955

88

15,611

110

16,073

107

29,269

115

36,937

120

44,724

102

34,724

98

39,126

65

44,261

Appendix A Statistical Tables



The regression model is solved for in the computer using the values of x and the values of log y where x is failures and y is liabilities. The resulting regression equation is:

*(Round your answer to 4 decimal places.)
**(Round your answer to 3 decimal places.)
***(Round your answer to 2 decimal places.)


log liabilities =

* +

* failures

F =

*** with p =

**, se =

*, R2 =

**, and adjusted R2 =

**. This model has modest predictability.

Question 37

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.

* +

** 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

.

Question 38

a. Explore trends in these data by using regression trend analysis. How strong are the models? Is the quadratic model significantly stronger than the linear trend model?

b. Use these data to develop forecast for the month 18 using a 4-month moving average.

c. Use simple exponential smoothing to forecast values for the month 10. Let ? = .3 and then let ? = .7. Which weight produces better forecasts?

d. Compute MAD for the forecasts obtained using a 4-month moving average and simple exponential smoothing with ? = .3 and then let ? = .7 and compare the results.

e. Determine seasonal effects using decomposition on these data. Let the seasonal effects have four periods. After determining the seasonal indexes, deseasonalize the data.

*(Round your answers to 1 decimal place.)
**(Round your answers to 2 decimal places.)
***(Round your answers to 3 decimal places.)
****(Round your answers to 4 decimal places.)
*****(Round your answers to 5 decimal places.)

a. The linear model:
Yield =

** +(

**) Month

F =

** p =

*** R2 =

*% se =

****

The quadratic model:

Yield =

* +(

***) Month + (

*****) Month2
F =

** p =

*** R2 =

*% se =

****

The

model is a strong model. The quadratic term adds some predictability but has a smaller t ratio than does the linear term.

b.

**

c. Using ? = .3 =

**
Using ? = .7 =

**

produces better forecasts based on MAD.

d. MAD for 4-month moving average =

****

MAD? = .3 =

****
MAD? = .7 =

****

Exponential smoothing with ? =

produces the lowest error.


(Round your answers to 2 decimal places.)

e. Seasonal Indexes:



1st

2nd

3rd

4th


FinalSeasonal Indexes:


1st

2nd

3rd

4th


1. Trend analysis for net sales and net income using 21114 as the base year.

 


 

Net Sales 131634 155:913 191329 211299

 

Net Income 4:431} 5:22? 6:295 6:621

 


 

Trend Percentages

 


 

Net Sales 100% 120% 139%...

 







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