|
| [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.
| 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 < 0 |
| [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.) |
| 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 < 0 |
|
| b-2. |
Find the p-value. (Round your answer to 4 decimal places.) |
| 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 < 0 |
| [removed] |
H0: β1 ≤ 0; HA: β1 > 0 |
|
| c-2. |
Find the p-value. (Round your answer to 4 decimal places.) |
| 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. |
|
| 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 < 0 |
| [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 < 0 |
| [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. |
|
|
|
