Part IV Practice Problems on Correlation and Regression

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Answer the following questions concerning the relationship between average sick days taken over the past 5 years by senior managers and their performance rating using the this data. Be sure to show all mathematics calculations.


Average Sick Days Taken 1995-1999

ID Number  AA1   AB2    AC3    AD4  AE5
Sick days taken 4 8 3 7 1
Performance Rating 8 2 7 4 9
1. Draw a scatter diagram of this data and calculate the coefficient of correlation to determine if average sick days taken over the last 5 years has an affect on a senior manager's most recent performance rating.

2.   Calculate the coefficient of determination and the coefficient of nondetermination.

3.   Using complete sentences, interpret your answers to questions 1 and 2.

4.   Could rho be zero at the .01 level of significance? Franklin Pierce college students may skip this question.

5.   Using the method of least squares, determine the regression equation for this data and draw it on your graph.

6.   Calculate the expected performance rating for a senior manager who averaged 5 absences per year over the 
      past 5 years.

1. -.952     

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2. 90.6% and 9.4%
3. High negative, 90.7% of the variability in rating is accounted for by variability in absences and 9.3% of the variability in rating is not accounted for by variability in absences.
4. No
5. Y.x = 10.4 - .964x (Hint: when calculating b, you have a double negative so 4.43 is added to 6.)
6. 5.58

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