stats

profiledaniela dentes
1.
value:
25.00 points
 
 
The following ANOVA table was obtained when estimating a multiple linear regression model. Use Table 4.
  
  ANOVAdfSSMSFSignificance F
  Regression2   22,894.43   11,447.22  ?0.0207        
  Residual17   39,588.56   2,328.74   
  Total19   62,482.99     

  
a-1.How many explanatory variables were specified in the model?
  
  Number of explanatory variables[removed]  
  
a-2.How many observations were used?
  
  Number of observations[removed]  
  
  b.Choose the appropriate hypotheses to determine whether the explanatory variables are jointly significant.
  
 
[removed]H0β1 = β2 = 0; HA: At least one β j ≠ 0
[removed]H0β1 = β2 = 0; HA: At least one β j > 0
[removed]H0β1 = β2 = 0; HA: At least one β j < 0

  c.Compute the value of the test statistic. (Round your answer to 2 decimal places.)

  Test statistic[removed]  

d-1.Find the p-value. (Round your answer to 4 decimal places.)

  p-value[removed]  

d-2.At the 5% significant level, what is the conclusion to the test?
  
 
[removed]Reject H0Picture the explanatory variables are jointly significant in explaining y.
[removed]Reject H0Picture the explanatory variables are not jointly significant in explaining y.
[removed]Do not reject H0Picture the explanatory variables are jointly significant in explaining y.
[removed]

Do not reject H0Picture the explanatory variables are not jointly significant in explaining y.

 

 

 

2.

value:
25.00 points
 
 

Akiko Hamaguchi is a manager at a small sushi restaurant in Phoenix, Arizona. Akiko is concerned that the weak economic environment has hampered foot traffic in her area, thus causing a dramatic decline in sales. In order to offset the decline in sales, she has pursued a strong advertising campaign. She believes advertising expenditures have a positive influence on sales. To support her claim, Akiko assumes the linear regression model as Sales = β0 + β1 Advertising + βUnemployment + ε. A portion of the regression results is shown in the accompanying table. Use Table 2 and Table 4.
 


 

  ANOVAdfSSMSFSignificance F
  Regression2   88.2574  44.1287  8.387  0.0040       
  Residual14   73.6638  5.2617   
  Total16   161.9212    


 

 CoefficientsStandard Errort Statp-valueLower 95%Upper 95%
  Intercept33.1260     6.9910      4.7384    0.0003    18.1300       48.12      
  Advertising0.0287     0.0080      3.5875    0.0029    0.0100       0.05      
  Unemployment−0.6758     0.3459      −1.9537    0.0710    −1.4200       0.0700      


 

a-1.Choose the appropriate hypotheses to test whether the explanatory variables jointly influence sales.
  
 
[removed]H0β1 = β2 = 0; HA: At least one β j < 0
[removed]H0β1 = β2 = 0; HA: At least one β j > 0
[removed]H0β1 = β2 = 0; HA: At least one β j ≠ 0


 

a-2.

Find the value of the appropriate test statistic. (Round your answer to 3 decimal places.)


 

  Test statistic[removed]  


 

a-3.At the 5% significance level, do the explanatory variables jointly influence sales?
  
 
[removed]Yes, since the F-test is significant.
[removed]Yes, since all t-tests are significant.
[removed]Both answers are correct.


 

b-1.Choose the hypotheses to test whether the unemployment rate is negatively related with sales.
  
 
[removed]H0β2 = 0; HAβ2 ≠ 0
[removed]H0β2 ≤ 0; HAβ2 > 0
[removed]H0β2 ≥ 0; HAβ2 < 0


 

b-2.

Find the p-value. (Round your answer to 4 decimal places.)


 

  p-value[removed]  


 

b-3.At the 1% significance level, what is the conclusion to the test?
  
 
[removed]Do not reject H0Picture the unemployment rate and sales are not negatively related.
[removed]Do not reject H0Picture the unemployment rate and sales are negatively related.
[removed]Do not reject H0Picture the unemployment rate and sales are related.
[removed]Do not reject H0Picture the unemployment rate and sales are not related.


 

c-1.Choose the appropriate hypotheses to test whether advertising expenditures are positively related to sales.
  
 
[removed]H0β1 = 0; HAβ1 ≠ 0
[removed]H0β1 ≥ 0; HAβ1 < 0
[removed]H0β1 ≤ 0; HAβ1 > 0


 

c-2.Find the p-value. (Round your answer to 4 decimal places.)


 

  p-value[removed]  


 

c-3.At the 1% significance level, what is the conclusion to the test?
  
 
[removed]Reject H0Picture advertising expenditures and sales are positively related.
[removed]Do not reject H0Picture advertising expenditures and sales are not positively related.
[removed]Do not reject H0Picture advertising expenditures and sales are positively related.
[removed]Reject H0Picture advertising expenditures and sales are not positively related.
3 --
 
 

For a sample of 20 New England cities, a sociologist studies the crime rate in each city (crimes per 100,000 residents) as a function of its poverty rate (in %) and its median income (in $1,000s). A portion of the regression results are as follows. Use Table 2 and Table 4.


 

  ANOVAdfSSMSFSignificance F
  Regression2   2,576.7  1,288.4  ?0.8163   
  Residual17   106,595.19  6,270.31   
  Total19   109,171.88    


 

 CoefficientsStandard Errort Statp-valueLower 95%Upper 95%
  Intercept800.10     126.6195      6.3189    0.0000  532.95   1,067.24    
  Poverty0.5779     6.3784      0.0906    0.9289  −12.88   14.04   
  Income−10.1429     16.1955      −0.6263    0.5395  −44.31   24.03    

 
 

 a.

Specify the sample regression equation. (Negative values should be indicated by a minus sign. Report your answers to 4 decimal places.)


 

  formula40.mml =[removed] + [removed] Poverty + [removed] Income


 

b-1.

Choose the appropriate hypotheses to test whether the poverty rate and the crime rate are linearly related.

  
 
[removed]H0β1 ≥ 0; HAβ1 < 0
[removed]H0β1 ≤ 0; HAβ1 > 0
[removed]H0β1 = 0; HAβ1 ≠ 0

        
 

b-2.At the 5% significance level, what is the conclusion to the hypothesis test?
  
 
[removed]Do not reject H0Picture the poverty rate and the crime rate are not linearly related.
[removed]Reject H0Picture the poverty rate and the crime rate are linearly related.
[removed]Do not reject H0Picture the poverty rate and the crime rate are linearly related.
[removed]Reject H0Picture the poverty rate and the crime rate are not linearly related.


 

c-1.

Construct a 95% confidence interval for the slope coefficient of income. (Negative values should be indicated by a minus sign. Round your intermediate calculations to 4 decimal places, "tα/2,df" value to 3 decimal places and final answers to 2 decimal places.)


 

  Confidence interval[removed] to [removed]  


 

c-2.

Using the confidence interval, determine whether income is significant in explaining the crime rate at the 5% significance level.

  
 
[removed]Income is significant in explaining the crime rate, since its slope coefficient does not significantly differ from zero.
[removed]Income is not significant in explaining the crime rate, since its slope coefficient does not significantly differ from zero.
[removed]Income is significant in explaining the crime rate, since its slope coefficient significantly differs from zero.
[removed]Income is not significant in explaining the crime rate, since its slope coefficient significantly differs from zero.


 

d-1.

Choose the appropriate hypotheses to determine whether the poverty rate and income are jointly significant in explaining the crime rate.

  
 
[removed]H0β1 = β2 = 0; HA: At least one β j < 0
[removed]H0β1 = β2 = 0; HA: At least one β j ≠ 0
[removed]H0β1 = β2 = 0; HA: At least one β j > 0


 

d-2.

At the 5% significance level, are the poverty rate and income jointly significant in explaining the crime rate?

  
 
[removed]No, since the null hypothesis is not rejected.
[removed]Yes, since the null hypothesis is rejected.
[removed]No, since the null hypothesis is rejected.
[removed]Yes, since the null hypothesis is not rejected.
    • 6 years ago
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