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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

Cost of goods sold

Inventory turnover ratio =

Average Inventory

3 60 days

Inventory turnover ratio

2,013 2014 2015 2016 201? 2013

CostofE'roods Sold 103:?25 150:255 111:562 191:838

Inventory...

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