1. Find the equation of the regression line for the given data. What is the predicted value of Y when X = -2? What is the predicted value of Y when X = 4?
X -7 -2 5 1 -1 -2 0 2 3 -3
Y -12 -8 9 1 -5 -6 -1 4 7 -8
2. The data below are the final exam scores of 10 randomly selected statistics students and the number of hours they studied for the exam. Find the equation of the regression line for the given data. Predict the final exam score for students who studied 4 hours. Predict th final exam score for students who studied 6 hours.
Hours (X) 3 5 2 8 2 4 4 5 6 3
Score (Y) 75 90 70 98 76 88 95 99 98 81
3. Find the correlation coefficient between X and Y. Is there a weak or strong, positive or negative correlation between X and Y?
X -5 -3 4 1 -1 -2 0 2 3 -4
Y -9 -7 8 2 -3 -5 -2 4 7 -7
4. A pharmaceutical company tested two new flu vaccines intended to boost immunity. In order to test the effectiveness of this drug, a one year study was done were at the beggining of the year three groups of eight individuals were given either Flu Shot 1, Flu Shot 2, or a placebo (a shot with only saline and no vaccine). The number of sick days from work each individual took was carefully recorded over the following year. Both flu shots were found to be completely safe with no side effects, but differed in terms of effectiveness. The data below gives the number of sick days for the individuals in each of the three groups.
Perform a one-way ANOVA analysis, testing at the 0.05 level. Also, calculate the mean number of sick days for each group. Describe your results. But equally important, also explain what you would do if you owned your own company. Would you pay for your employers to receive Flu Shot 1 or Flu Shot 2 in order to keep their number of sick days down? If so, which one would you choose? Would you choose either vaccine only if it was very cheap or would you be willing to invest a lot into the vaccine for your employees? Explain your reasoning.
Group Sick days per year
Placebo 7 4 6 8 6 6 2 9
Flu Shot 1 5 3 3 5 4 7 3 3
Flu Shot 2 2 4 1 2 2 1 2 5
Submit your work by the module due date, if you are having difficulty please contact your professor.
Case Assignment Expectations:
Use information from the modular background readings as well as any good quality resource you can find. Please cite all sources and provide a reference list at the end of your paper.
The following items will be assessed in particular:
- Your ability to explain the limitations of the linear regression method.
- Your ability to describe ANOVA and identify when the ANOVA method should be used.
- Your ability to describe the correlation analysis and identify when the coefficient of correlation should be calculated.
- Your ability to identify when the Least Squares method should be used.