[removed]  Do not reject H_{0} 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 = β_{0} + β_{1} Advertising + β_{2 }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  pvalue  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 

a1.  Choose the appropriate hypotheses to test whether the explanatory variables jointly influence sales.     [removed]  H_{0}: β_{1} = β_{2} = 0; H_{A}: At least one β _{j} < 0  [removed]  H_{0}: β_{1} = β_{2} = 0; H_{A}: At least one β _{j} > 0  [removed]  H_{0}: β_{1} = β_{2} = 0; H_{A}: At least one β _{j} ≠ 0 

a2.  Find the value of the appropriate test statistic. (Round your answer to 3 decimal places.) 
a3.  At the 5% significance level, do the explanatory variables jointly influence sales?     [removed]  Yes, since the Ftest is significant.  [removed]  Yes, since all ttests are significant.  [removed]  Both answers are correct. 

b1.  Choose the hypotheses to test whether the unemployment rate is negatively related with sales.     [removed]  H_{0}: β_{2} = 0; H_{A}: β_{2} ≠ 0  [removed]  H_{0}: β_{2} ≤ 0; H_{A}: β_{2} > 0  [removed]  H_{0}: β_{2} ≥ 0; H_{A}: β_{2} < 0 

b2.  Find the pvalue. (Round your answer to 4 decimal places.) 
b3.  At the 1% significance level, what is the conclusion to the test?     [removed]  Do not reject H_{0} the unemployment rate and sales are not negatively related.  [removed]  Do not reject H_{0} the unemployment rate and sales are negatively related.  [removed]  Do not reject H_{0} the unemployment rate and sales are related.  [removed]  Do not reject H_{0} the unemployment rate and sales are not related. 

c1.  Choose the appropriate hypotheses to test whether advertising expenditures are positively related to sales.     [removed]  H_{0}: β_{1} = 0; H_{A}: β_{1} ≠ 0  [removed]  H_{0}: β_{1} ≥ 0; H_{A}: β_{1} < 0  [removed]  H_{0}: β_{1} ≤ 0; H_{A}: β_{1} > 0 

c2.  Find the pvalue. (Round your answer to 4 decimal places.) 
c3.  At the 1% significance level, what is the conclusion to the test?     [removed]  Reject H_{0} advertising expenditures and sales are positively related.  [removed]  Do not reject H_{0} advertising expenditures and sales are not positively related.  [removed]  Do not reject H_{0} advertising expenditures and sales are positively related.  [removed]  Reject H_{0} 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  pvalue  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 
b1.  Choose the appropriate hypotheses to test whether the poverty rate and the crime rate are linearly related.     [removed]  H_{0}: β_{1} ≥ 0; H_{A}: β_{1} < 0  [removed]  H_{0}: β_{1} ≤ 0; H_{A}: β_{1} > 0  [removed]  H_{0}: β_{1} = 0; H_{A}: β_{1} ≠ 0 

b2.  At the 5% significance level, what is the conclusion to the hypothesis test?     [removed]  Do not reject H_{0} the poverty rate and the crime rate are not linearly related.  [removed]  Reject H_{0} the poverty rate and the crime rate are linearly related.  [removed]  Do not reject H_{0} the poverty rate and the crime rate are linearly related.  [removed]  Reject H_{0} the poverty rate and the crime rate are not linearly related. 

c1.  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] 
c2.  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. 

d1.  Choose the appropriate hypotheses to determine whether the poverty rate and income are jointly significant in explaining the crime rate.     [removed]  H_{0}: β_{1} = β_{2} = 0; H_{A}: At least one β _{j} < 0  [removed]  H_{0}: β_{1} = β_{2} = 0; H_{A}: At least one β _{j} ≠ 0  [removed]  H_{0}: β_{1} = β_{2} = 0; H_{A}: At least one β _{j} > 0 

d2.  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. 

