The number of COVID cases in a county tends to be related to two things: 1) the population of the county, and 2) the number of vaccinated individuals. Use the data below to investigate this connection. The variables are COVID cases, number of fully vaccinated people (1000s), and population (1000s). Vaccinations (1000s) Population (1000s) Cases 6 17 1257 3 21 1526 9 9 605 9 13 475 5 6 13 6 19 1378 8 24 1794 6 9 787 9 18 491 8 23 1754 11 21 470 5.5 6 968 10 13 650 11 13 781 7 18 1484 1) Develop the estimated regression equation relating county COVID cases to vaccinations and populations. Write it in the form CASES = ___ + ___ VAX + ___ POP, where you fill in the blanks. Round to two decimals. 2) Is the county population a significant factor in determining county COVID cases? Why or why not? Use ax 0.05 to test the level of significance. 3) Predict the number of COVID cases for a county with a population of 12,000 and 8,000 vaccinations. 4) Does the estimated regression equation provide a good fit to the data? Explain 5) Now develop the estimated regression equation relating county COVID cases to just vaccinations. Write it in the form CASES = ____ + ____ VAX, where you fill in the blanks. Round to two decimals. 6) What is the adjusted R2 from question 5? 7) Which estimated equation do you prefer to explain COVID cases - from question 1 or question 5? Use your answers from questions 4 and 6 to explain. 8) Should either vaccinations or population be dropped from the original estimated regression in question 1? Explain. (Hint: using previous answers will be helpful here.) 9) For this part, ignore your previous results. Suppose instead when you estimated question 1 you found CASES = 1043 - 100VAX +67POP. Interpret b1 and b2 in this new estimated regression equation. Do the results make sense? Why or why not? Note: you need to answer all three parts - interpret, does this make sense, explanation. 10) Some people believe that political affiliation is related to the number of county COVID cases. Suppose you wanted to test this theory and include whether or not a county voted democrat in the regression. How exactly would you include this information in the regression analysis? (Note: please describe what the data would look like since this is qualitative information.)
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The number of COVID cases in a county tends to be related to two things: 1) the population of the county, and 2) the number of vaccinated individuals. Use the data below to investigate this connection. The variables are COVID cases, number of fully vaccinated people (1000s), and population (1000s).
| Vaccinations (1000s) | Population (1000s) | Cases |
| 6 | 17 | 1257 |
| 3 | 21 | 1526 |
| 9 | 9 | 605 |
| 9 | 13 | 475 |
| 5 | 6 | 13 |
| 6 | 19 | 1378 |
| 8 | 24 | 1794 |
| 6 | 9 | 787 |
| 9 | 18 | 491 |
| 8 | 23 | 1754 |
| 11 | 21 | 470 |
| 5.5 | 6 | 968 |
| 10 | 13 | 650 |
| 11 | 13 | 781 |
| 7 | 18 | 1484 |
1) Develop the estimated regression equation relating county COVID cases to vaccinations and populations. Write it in the form CASES = ___ + ___ VAX + ___ POP, where you fill in the blanks. Round to two decimals.
2) Is the county population a significant factor in determining county COVID cases? Why or why not? Use ax 0.05 to test the level of significance.
3) Predict the number of COVID cases for a county with a population of 12,000 and 8,000 vaccinations.
4) Does the estimated regression equation provide a good fit to the data? Explain
5) Now develop the estimated regression equation relating county COVID cases to just vaccinations. Write it in the form CASES = ____ + ____ VAX, where you fill in the blanks. Round to two decimals.
6) What is the adjusted R2 from question 5?
7) Which estimated equation do you prefer to explain COVID cases - from question 1 or question 5? Use your answers from questions 4 and 6 to explain.
8) Should either vaccinations or population be dropped from the original estimated regression in question 1? Explain. (Hint: using previous answers will be helpful here.)
9) For this part, ignore your previous results. Suppose instead when you estimated question 1 you found CASES = 1043 - 100VAX +67POP. Interpret b1 and b2 in this new estimated regression equation. Do the results make sense? Why or why not?
Note: you need to answer all three parts - interpret, does this make sense, explanation.
10) Some people believe that political affiliation is related to the number of county COVID cases. Suppose you wanted to test this theory and include whether or not a county voted democrat in the regression. How exactly would you include this information in the regression analysis? (Note: please describe what the data would look like since this is qualitative information.)
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