stats

daniela dentes

Main

Home >Homework Answsers >Mathematics homework help

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]

Choose the appropriate hypotheses to determine whether the explanatory variables are jointly significant.

[removed]	H₀: β₁ = β₂ = 0; H_A: At least one β _j ≠ 0
[removed]	H₀: β₁ = β₂ = 0; H_A: At least one β _j > 0
[removed]	H₀: β₁ = β₂ = 0; H_A: 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 H₀

the explanatory variables are jointly significant in explaining y.

[removed]

Reject H₀

the explanatory variables are not jointly significant in explaining y.

[removed]

Do not reject H₀

the explanatory variables are jointly significant in explaining y.

[removed]

Do not reject H₀ the explanatory variables are not jointly significant in explaining y.

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 + β₂Unemployment + 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]	H₀: β₁ = β₂ = 0; H_A: At least one β _j < 0
[removed]	H₀: β₁ = β₂ = 0; H_A: At least one β _j > 0
[removed]	H₀: β₁ = β₂ = 0; H_A: 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]	H₀: β₂ = 0; H_A: β₂ ≠ 0
[removed]	H₀: β₂ ≤ 0; H_A: β₂ > 0
[removed]	H₀: β₂ ≥ 0; H_A: β₂ < 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 H₀ the unemployment rate and sales are not negatively related.
[removed]	Do not reject H₀ the unemployment rate and sales are negatively related.
[removed]	Do not reject H₀ the unemployment rate and sales are related.
[removed]	Do not reject H₀ 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]	H₀: β₁ = 0; H_A: β₁ ≠ 0
[removed]	H₀: β₁ ≥ 0; H_A: β₁ < 0
[removed]	H₀: β₁ ≤ 0; H_A: β₁ > 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 H₀ advertising expenditures and sales are positively related.
[removed]	Do not reject H₀ advertising expenditures and sales are not positively related.
[removed]	Do not reject H₀ advertising expenditures and sales are positively related.
[removed]	Reject H₀ 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.)

=[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]	H₀: β₁ ≥ 0; H_A: β₁ < 0
[removed]	H₀: β₁ ≤ 0; H_A: β₁ > 0
[removed]	H₀: β₁ = 0; H_A: β₁ ≠ 0

b-2.

At the 5% significance level, what is the conclusion to the hypothesis test?

[removed]	Do not reject H₀ the poverty rate and the crime rate are not linearly related.
[removed]	Reject H₀ the poverty rate and the crime rate are linearly related.
[removed]	Do not reject H₀ the poverty rate and the crime rate are linearly related.
[removed]	Reject H₀ 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, "t_α_/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]	H₀: β₁ = β₂ = 0; H_A: At least one β _j < 0
[removed]	H₀: β₁ = β₂ = 0; H_A: At least one β _j ≠ 0
[removed]	H₀: β₁ = β₂ = 0; H_A: 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.

12 years ago
07.12.2014
10

Report issue

Answer(0)

Bids(0)

other Questions(10)