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https://docs.google.com/spreadsheets/d/1obdmVSD1CXm2iY5buTf4rbg9fIYsNGAb/edit#gid=1485328872
Energy Economics: The quantity of Gas/Oil exports in thousands of metric tons for the year 2018 are available for 100 countries from six of the seven continents around the world (Europe (EU), Africa (AF), Asia (AS), South America (SA), Oceania (OC), and North America (NA)). Fit a regression model to predict quantity of gas/oil exports (Quantity) from the continent within which each country resides. Code the Continent variable so that North America serves as the reference group. The data are available in the worksheet entitled "GASOIL". (a) State the model equation. O QUANTITY = Bo + BINA O QUANTITY = Bo + B1EU + B2AF + B3AS + BASA + B5NA O QUANTITY = Bo + B1EU + B2AF + B3AS + BASA + B5OC O QUANTITY = Bo + B1CONTINENT O QUANTITY = Bo + B1EU + B2AF + B3CONTINENT O QUANTITY = Bo + B1EU + B2AF + B3AS + BASA + 35CONTINENT X (b) Is there a difference in quantity of gas/oil exports among the different continents? Perform a hypothesis test to answer this question. Use a 1% level of significance. State the hypotheses to be tested. O Ho: B1 = $2 = 0 Ha: At least one of the coefficients is not equal to 0. O Ho: B3 = B4 = 0 Ha: At least one of the coefficients is not equal to 0. O Ho: B1 = B2 = B3 = B4 = 0 Ha: At least one of the coefficients is not equal to 0. O Ho: At least one of the coefficients is not equal to 0. Ha: B3 = B4 = 0 O Ho: B1 = B2 = B3 = B4 = B5 = 0 Ha: At least one of the coefficients is not equal to 0. O Ho: None of the coefficients are equal to 0. Ha: B3 = B4 = B5 = 0State the reduced model equation. O QUAN'ITI'Y = BICONTINENT 0 QUANTITY = 12,) O QUAN'ITrY = {30 + mm + BZAF + B3AS + E4SA + soc 0 QUANTITY = 5.3 + EiEU + EzAF + B3As + B4SA + ESNA QUANTITY = [3.3 + lcoN'lTNENT O QUAN'ITI'Y = 50 + 51M State the appropriate test statistic name, degrees of freedom, test statistic value, and the associated p-value (Enter the degrees of freedom as a whole number, the test statistic value to three decimal places, and the pvalue to four decimal places). H'I (I lrl l)=l lrpwv State your decision. Fail to reject the null hypothesis. There is a signicant difference in quantity of gas/oil exports among the different continents at the a: = .01 level. 0 Reject the null hypothesis. There is a signicant difference in quantity of gas/oil exports among the different continents at the a = .01 level. 0 Reject the null hypothesis. There is no signicant difference in quantity of gas/oil exports among the different continents at the a = .01 level. 0 Fail to reject the null hypothesis. There is no signicant difference in quantity of gas/oil exports among the different continents at the a = .01 level. X (c) Regardless of your conclusions above, use the full model specied above (with all the variables) to answer the following questions. What is the predicted quantity of gas/oil exports for a country in Europe? (Round your answer to three decimal places.) What is the predicted quantity of gas/oil exports for a country in North America? (Round your answer to three decimal places.) What is the predicted quantity of gas/oil exports for a country in Asia? (Round your answer to three decimal places.) (d) How do you account for the differences in the estimates in part (c)? 0 There are major differences in the quantity of gas/oil exports among the different continents and, according to the Ftest, these differences are an important phenomenon that is generalizable to the entire population of countries. 0 Continent explains all of the variation in the quantity of gas/oil exports among countries. @ Even though there appears to be substantial differences in the quantity of gas/oil exports among the different continents, this is indistinguishable from sampling error (most likely due to very large within-continent variation) and, therefore, probably not an important phenomenon that is generalizable to the entire population of countries. 0 Continent explains none of the variation in the quantity of gas/oil exports among countries. (e) Regardless of your conclusions above, use the full model specied above (with all the variables) to answer the following questions. Choose the proper interpretation of the coefcient for Europe from your analysis above by mentally inserting the ABSOLUTE VALUE of that number in the blanks below. 0 Countries in Europe are predicted to produce on average thousands of metric tons of gas/oil exports less than the average North American country. 0 Countries in Europe are predicted to produce on average thousands of metric tons of gas/oil exports less than the average African country. 0 Countries in Europe are predicted to produce on average thousands of metric tons of gas/oil exports less than the average South American country. Countries in Europe are predicted to produce on average thousands of metric tons of gas/oil exports more than the average North American country. 0 Countries in Europe are predicted to produce on average thousands of metric tons of gas/oil exports more than the average South American country. 0 Countries in Europe are predicted to produce on average thousands of metric tons of gas/oil exports more than the average African country. X Provide a 99% condence interval for the coefcient for Europe. (Enter your answers to three decimal places.) (E's) merrier-ms Countries in Europe are predicted to produce on average thousands of metric tons of gas/oil exports less than the average North American country. Countries in Europe are predicted to produce on average thousands of metric tons of gas/oil exports less than the average African country. O Countries in Europe are predicted to produce on average thousands of metric tons of gas/oil exports less than the average South American country. Countries in Europe are predicted to produce on average thousands of metric tons of gas/oil exports more than the average North American country. O Countries in Europe are predicted to produce on average thousands of metric tons of gas/oil exports more than the average South American country. O Countries in Europe are predicted to produce on average thousands of metric tons of gas/oil exports more than the average African country. X Provide a 99% confidence interval for the coefficient for Europe. (Enter your answers to three decimal places.) metric tons Choose the proper interpretation of the confidence interval for the coefficient for Europe from your analysis above. Because the confidence interval for Europe includes zero, there is no statistically significant difference in the quantity of gas/oil exports between Europe and Africa at the 99% confidence level. Because the confidence interval for Europe does not include zero, there is a statistically significant difference in the quantity of gas/oil exports between Europe and Africa at the 99% confidence level. O Because the confidence interval for Europe includes zero, there is no statistically significant difference in the quantity of gas/oil exports between Europe and North America at the 99% confidence level. Because the confidence interval for Europe includes zero, there is no statistically significant difference in the quantity of gas/oil exports between Europe and the other continents at the 99% confidence level. O Because the confidence interval for Europe does not include zero, there is a statistically significant difference in the quantity of gas/oil exports between Europe and the other continents at the 99% confidence level. Because the confidence interval for Europe does not include zero, there is a statistically significant difference in the quantity of gas/oil exports between Europe and North America at the 99% confidence level. X
