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value: 25.00 points The following ANOVA table was obtained when estimating a multiple li

value: 25.00 points The following ANOVA table was obtained when estimating a multiple li

value:
25.00 points  

The following ANOVA table was obtained when estimating a multiple linear regression model. Use Table 4.

  

  ANOVA df SS MS F Significance F
  Regression 2    22,894.43    11,447.22   ? 0.0207        
  Residual 17    39,588.56    2,328.74    
  Total 19    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 

 

  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.
 


 

  ANOVA df SS MS F Significance F
  Regression 2    88.2574   44.1287   8.387   0.0040       
  Residual 14    73.6638   5.2617    
  Total 16    161.9212      


 

  Coefficients Standard Error t Stat p-value Lower 95% Upper 95%
  Intercept 33.1260      6.9910       4.7384     0.0003     18.1300        48.12      
  Advertising 0.0287      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 
[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 


 

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 
[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.


 

  ANOVA df SS MS F Significance F
  Regression 2    2,576.7   1,288.4   ? 0.8163   
  Residual 17    106,595.19   6,270.31    
  Total 19    109,171.88      


 

  Coefficients Standard Error t Stat p-value Lower 95% Upper 95%
  Intercept 800.10      126.6195       6.3189     0.0000   532.95    1,067.24    
  Poverty 0.5779      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 
[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 
[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.
Abhinav 29-Nov-2019

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