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Chapter 14Extra. Regression

Consider the following table which shows the scores of another twelve students on the final exams of four courses:
   Course 1  Course 2
 a  27.68  23.59
 b  65.52  75.85
 c  42.39  27.68
 d  35.66  44.79
 e  75.82  56.68
 f  23.59  31.94
 g  54.48  42.39
 h  47.45  65.51
 i  31.94  35.61
 j  44.79  38.35
 k  38.35  46.45
 l  16.55  21.79
   Course 3  Course 4
 a 68.68 26.68
 b 25.62 63.51
 c 35.30 35.39
 d 67.46 35.61
 e 25.74 73.82
 f 67.72 75.59
 g 25.54 72.58
 h 28.39 47.45
 i 67.25 37.94
 j 25.46 35.79
 k 26.02 41.35
 l 64.54 24.29

 

Use the data for the first two courses for Questions 1 - 11. Use the data for the 3rd and 4th courses for Questions 12 - 16.

1. Calculate the means and standard deviations of the scores in the first two courses.

   course 1  course 2
 means    
 standard deviations    

2. Calculate Pearson's r for the scores in the first two courses.

 

3. Calculate a regression equation, using the scores on the first course as the independent variable and the scores on the second course as the dependent variable.

First the slope:

Then the intercept:

Now the equation:


4. Draw a scatterplot for the data for the first two courses and draw the regression line on the graph. Label the Y-intercept.

5. Locate the means of the first two courses on the graph and determine whether the regression line passes through the two means.

6. What is the coefficient of determination for the data for the first two courses? What does it mean?

7. What is the slope of the regression line? What does the slope tell you about your variables and how they are related to one another?

8. Calculate the residuals for students c, f, g, and k.

   Course 1  Course 2    residual
 c  42.39  27.68    
 f  23.59  31.94    
h  47.45  65.51    
 k  38.35  46.45    


10. If a student received a score of 64 in the first course, what would you expect the student's score in the second course would be?

You would expect it to be:

(what is the equation you use?)

which is:

 


11. If a student received a score of 100 in the first course, what would you expect the student's score in the second course would be?

 

12. Calculate the means and standard deviations of the scores in the third and fourth courses.

   Course 3 x  Course 4 y
 means    
 standard deviations    


13. Calculate Pearson's r for the scores in the third and fourth courses.



14. Calculate a regression equation, using the scores on the third course as the independent variable and the scores on the fourth course as the dependent variable.

First the slope:

 

Then the intercept:

 

Now the equation:

 

15. Draw a scatterplot for the data for the third and fourth courses and draw the regression line on the graph. Label the intercept.



16. After looking at the scatterplot from Question 15, discuss the appropriateness of the analysis you did in Question 14. What is the problem? What are the consequences of doing this kind of analysis on data like the data for the third and fourth courses?