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1. Determine the equation of 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 given below are the final exam scores of 10 randomly chosen statistics students and the number of hours they studied for exam. Determine the equation of the regression line for the given data. Predict final exam score for students who studied 4 hours.  Predict 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. Determine 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. To test the efficiency of this drug, a one year study was done were at the starting 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 given below gives the number of sick days for the individuals in each of the three groups.

Carry out a one-way ANOVA analysis, testing at the 0.05 level.  Also, compute the mean number of sick days for each group. describe your results.  But equally important, also describe what you will do if you owned your own company.  will 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 will you select? Will 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?  Describeyour 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

Statistics and Probability, Statistics

  • Category:- Statistics and Probability
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