Example problems for correlation and regression. For each problem you should draw a scatterplot, calculate the correlation coefficent, interpret the coeffeicent, and calculate a regression line. Use SPSS for problems 4 and 5

1. The following data are scores from 15 subjects on a College Aptitude Test (CAT) and the number of semester hours of science courses taken in high school (# of SC).

Subject
CAT
# of SH
1
23
15
2
27
18
3
30
18
4
19
12
5
18
9
6
21
9
7
17
6
8
21
12
9
27
15
10
29
12
11
5
12
12
22
12
13
26
15
14
25
12
15
24
18

 

 

 

2. A random sample of freshman psychology majors ranked various fields of psychology according to vocational attractiveness. The students again ranked the fields when they were seniors.

Field
Freshman
Senior
Social
9
2
Experimental
7
6
Human factors
6
7
Clinical
1
1
Statistics
8
8
Industrial
3
9
Educational
4
8
Counseling
5
1

 

 

3. A psychiatric social worker and an occupational therapist ranked 11 Veteran's Administration patients with respect to extent of recovery following 3 months of therapy.

 

Patient
Social Worker
Occupational Therapist

 

1

 

7

 

7

 

2

 

2

 

1

 

3

 

1

 

2

 

4

 

3

 

5

 

5

 

8

 

9

 

6

 

10

 

10

 

7

 

4

 

3

 

8

 

9

 

8

 

9

 

11

 

11

 

10

 

6

 

6

 

11

 

5

 

4

 

 

 

4. Below are three scores for each of nine subjects. Compute the correlation between A and B, A and C, and B and C. Add five to each score in distribution A and then multiply by 2. Re-compute the correlation between A and B. Explain the effect of changing scales on the correlation. Use SPSS to complete this problem. Double click on the graphs produced by SPSS and try to make the graphs look nice (e.g., center the variable names) !

Subject

 

A

 

B

 

C

 

1

 

2

 

2

 

6

 

2

 

0

 

7

 

3

 

3

 

5

 

3

 

10

 

4

 

6

 

0

 

3

 

5

 

6

 

1

 

6

 

6

 

8

 

3

 

1

 

7

 

0

 

7

 

5

 

8

 

3

 

2

 

7

 

9

 

8

 

1

 

10

 5. Perform a multiple regression analysis predicting number of hours of school work from age, number of hours worked outsideof school, and distance to school. What happens to the ability to predict if number of hours worked outside of school, and distance to school are removed from the eqaution? Provide me with the regressions equations, r, and stderr, for each model and indicate whether or not there was a significant difference between the two models.