Akiko Hamaguchi is a manager at a small sushi restaurant in

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 = ₀ + ₁ Advertising + ₂ Unemployment + . A portion of the regression results is shown in the accompanying table. Use Table 2 and Table 4.

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

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 = 0 + 1 Advertising + 2 Unemployment + . A portion of the regression results is shown in the accompanying table. Use Table 2 and Table 4.

Solution

ANOVA

df

SS

MS

F

Significance F

  Regression

2   

69.7974

34.8987

8.851

0.0033       

  Residual

14   

55.2038

3.9431

  Total

16   

125.0012

Coefficients

Standard Error

t Stat

p-value

Lower 95%

Upper 95%

  Intercept

14.6660     

4.7989      

3.0561    

0.0085    

4.3700       

24.96      

  Advertising

0.0320     

0.0086      

3.7209    

0.0022    

0.0100       

0.05      

  Unemployment

0.6725     

0.2585      

2.6015    

0.0209    

1.2300       

0.1200    

a-1.

Choose the appropriate hypotheses to test whether the explanatory variables jointly influence sales.

H₀: ₁ = ₂ = 0; H_A: At least one _j < 0

H₀: ₁ = ₂ = 0; H_A: At least one _j > 0

H₀: ₁ = ₂ = 0; H_A: At least one _j 0

( alternate hypothesis is not equal to zero)

a-2.

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

F value in the ANOVA table is the test value.

  Test statistic   8.851

ANOVA	df	SS	MS	F	Significance F
Regression	2	69.7974	34.8987	8.851	0.0033
Residual	14	55.2038	3.9431
Total	16	125.0012