Chat Now

# 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] H0: β1 = β2 = 0; HA: At least one β j ≠ 0 [removed] H0: β1 = β2 = 0; HA: At least one β j > 0 [removed] H0: β1 = 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]

 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.

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 + β2 Unemployment + 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; HA: At least one β j [removed] H0: β1 = β2 = 0; HA: At least one β j > 0 [removed] H0: β1 = 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] H0: β2 = 0; HA: β2 ≠ 0 [removed] H0: β2 ≤ 0; HA: β2 > 0 [removed] H0: β2 ≥ 0; HA: β2

 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; HA: β1 ≠ 0 [removed] H0: β1 ≥ 0; HA: β1 [removed] H0: β1 ≤ 0; HA: β1 > 0

 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; HA: β1 [removed] H0: β1 ≤ 0; HA: β1 > 0 [removed] H0: β1 = 0; HA: 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, "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] H0: β1 = β2 = 0; HA: At least one β j [removed] H0: β1 = β2 = 0; HA: At least one β j ≠ 0 [removed] H0: β1 = 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 Get solution