ANOVA & Least Squares

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