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Question 34 Determine the Pearson productmoment correlation
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Question 35
 

(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 pvalue =
. Thus, there is overall significance at ? = .01. One of the three predictors is significant. Gasoline Consumption has a t = 2.67 with pvalue of
which is statistically significant at ? = .05. The pvalues 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 fourquadrant approach as a resource. Compare your models.
 

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 =
**, s_{e} =
*, R^{2} =
**, and adjusted R^{2} =
**. 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 timeseries data to develop an autoregression model with a oneperiod lag. Now try an autoregression model with a twoperiod lag. Discuss the results and compare the two models.
* +
** lag 1
F =
** p =
*** R^{2} =
*% adjusted R^{2} =
*% s_{e} =
**
The model with 2  period lag:
Housing Starts =
**** +
** lag 2
F =
** p =
*** R^{2} =
*% adjusted R^{2} =
*% s_{e} =
**
The model with
is better model with a
R^{2}. 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 4month 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 4month 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 =
*** R^{2} =
*% s_{e} =
****
The quadratic model:
Yield =
* +(
***) Month + (
*****) Month^{2}
F =
** p =
*** R^{2} =
*% s_{e} =
****
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 4month moving average =
****
MAD_{? = .3 }=
****
MAD_{? = .7 }=
****
Exponential smoothing with ? =
produces the lowest error.
(Round your answers to 2 decimal places.)
e. Seasonal Indexes:
1^{st}  
2^{nd}  
3^{rd}  
4^{th} 
FinalSeasonal Indexes:
1^{st}  
2^{nd}  
3^{rd}  
4^{th} 
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This question was answered on: Feb 21, 2020
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