An Econometrics student is using data for a sample of 27 Belizean firms to investigate the relationship between annual profits (Y), measured in millions of BZ\$ per year, and annual sales revenues (X), measured in billions of BZ \$ per year. The population regression equation of interest is: Yi=1+2Xi+Ui Preliminary analysis of the sample data produces the following sample information: i=1nYi=12,767i=1nXi2=19,058.49i=1nyixi=129,363.77i=1nXi=570.175i=1nYiXi=398,972.09i=1nyi2=5,853,157i=1nYi2=11,890,057i=1nU^i2=3,468,497.03i=1nxi2=7,017.77 where yi=YiY and xi=XiX for i=1,2,3n. Use the above sample information to answer all the following questions: 1. Compute the OLS estimates of the intercept and slope coefficients. 2. Provide an interpretation of the slope coefficient estimate. 3. Compute the value of R2 and provide an interpretation of this value. 4. Calculate the estimated variances of ^1 and ^2. 5. Perform a test of the null hypothesis H0:2=0 against the alternative hypothesis H1:2=0 at the 5% significance level. State the decision rule you use, and the inference you would draw from the test. Would you draw the same inference if you performed the test at the 1% significance level? 6. Compute the two-sided 95% confidence interval for the slope coefficient 2. 7. Perform a test of the null hypothesis H0:210 against the alternative hypothesis H1:2>10 at the 5% significance level. State the decision rule you use, and the inference you would draw from the test. Would you draw the same inference if you performed the test at the 1% significance level? 8. Perform a test of the null hypothesis of no regression at the 5% significance level. An Econometrics student is using data for a sample of 27 Belizean firms to investigate the relationship between annual profits (Y), measured in millions of BZ\$ per year, and annual sales revenues (X), measured in billions of BZ \$ per year. The population regression equation of interest is: Yi=1+2Xi+Ui Preliminary analysis of the sample data produces the following sample information: i=1nYi=12,767i=1nXi2=19,058.49i=1nyixi=129,363.77i=1nXi=570.175i=1nYiXi=398,972.09i=1nyi2=5,853,157i=1nYi2=11,890,057i=1nU^i2=3,468,497.03i=1nxi2=7,017.77 where yi=YiY and xi=XiX for i=1,2,3n. Use the above sample information to answer all the following questions: 1. Compute the OLS estimates of the intercept and slope coefficients. 2. Provide an interpretation of the slope coefficient estimate. 3. Compute the value of R2 and provide an interpretation of this value. 4. Calculate the estimated variances of ^1 and ^2. 5. Perform a test of the null hypothesis H0:2=0 against the alternative hypothesis H1:2=0 at the 5% significance level. State the decision rule you use, and the inference you would draw from the test. Would you draw the same inference if you performed the test at the 1% significance level? 6. Compute the two-sided 95% confidence interval for the slope coefficient 2. 7. Perform a test of the null hypothesis H0:210 against the alternative hypothesis H1:2>10 at the 5% significance level. State the decision rule you use, and the inference you would draw from the test. Would you draw the same inference if you performed the test at the 1% significance level? 8. Perform a test of the null hypothesis of no regression at the 5% significance level