Correlation and Regression
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This week we are working on correlation and regression.
All work that can be done in SPSS must be submitted in that format.
1. Dr. Allen suspects a strong correlation between math anxiety and performance in statistics. To test that hypothesis he collects the following data.
Math Anxiety 1st Exam Score
78 42
68 58
82 38
56 75
23 82
22 85
34 49
20 86
53 54
65 53
30 84
a. Conduct and interpret the appropriate analysis to determine if there is a relationship between math anxiety and performance in statistics.
b. Construct the appropriate graph to show the relationship between math anxiety and exam score.
c. If a student scores a 49 on the Math Anxiety test, what would be the predicted score on the first exam?
d. If a student scores an 85 on the Math Anxiety, what would be the predicted score on the first exam?
2. A professor develops a scale that he believes measures spiritual maturity. To establish the reliability of his scale he administers the test to a group of students at 6 week intervals.
Test Retest
45 35
68 75
51 52
78 60
48 75
80 72
78 85
70 78
a. Is the test measuring a stable construct? Conduct and interpret the appropriate analysis to determine reliability of the test.
b. Construct the appropriate graph to illustrate the data.
3. A University Counseling Clinic is interested in predicting the levels of depression from the number of social events attended per week by a sample of their clients. The data are below:
Social events per week Depression Scores
0 15
2 3
2 12
1 11
3 5
1 8
2 15
0 13
3 2
3 4
4 2
1 8
1 10
2 8
a. Conduct and interpret the appropriate analysis to determine if there is a relationship between number of social events attended and depression scores.
b. Create the appropriate graph to illustrate the relationship between these two variables.
c. What would you predict for a depression score for someone who attended 2 events per week?
d. What would you predict for a depression score if someone attended 4 events per week?
4. Students in General Psychology were allowed to sign up for one of two sections of that course. One section has a virtual lab component to it, in which they are given additional assignments to supplement the lecture content. These exercises consist of various games, demonstrations etc., that the students complete utilizing the CD-ROM that comes with their textbook. The other section of the course is a regular lecture class, with no supplemental lab exercises
No lab Virtual Lab
85 70
74 84
94 75
71 80
73 94
75 87
82 90
48 75
65 92
70 90
a. Conduct and interpret the appropriate analysis to determine if the virtual lab group has significantly higher scores.
b. Construct the appropriate graph to illustrate the differences in the two groups.
c. From the professor's experience, he knows that students who score in the top 10% of the class are great candidates for lab assistants in the future. What score in the Virtual Lab group would indicate such a student?
5. The same students from the above scenario who are in the General Psychology class with the Virtual Lab exercises are asked to rate their opinion of the lab experiences.
Virtual Lab Opinion
70 15
84 18
75 12
80 17
94 20
87 18
90 15
75 17
92 16
90 10
a. Conduct and interpret the appropriate statistical analysis to determine if there is a relationship between their opinion of the lab and their final exam grade? (A high # reflects favorable opinion).
b. Construct the appropriate graph to illustrate the relationship between the variables.
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Solution Summary
The solution addresses correlation and regression.
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* Pearson and Spearman both measure the correlation (r). You can get them in SPSS by doing a regression analysis (the correlation will show up in one of several boxes of output).
* The regression equation is y = bx + a. The b and the a show up in another one of the output boxes in SPSS (in the table titled "Coefficients"). In question 1a, look at the regression analysis output and see how the numbers compare to the regression equation that I wrote out.
* Reliability is just a special use for a correlation coefficient. There's a separate reliability test in SPSS (i.e. it's its own test, it's not under regression analysis).
* Ordinal data are data that are ordered, but where differences between numbers don't mean anything. For example, ratings from 1 - 5 are ordinal data: if you rate something a 4, it means that you like it more than something you rate a 2, but it doesn't necessarily mean that you like it twice as much; the difference between something rated a 2 instead of a 1 is not necessarily the same as the difference between something rated a 5 instead of a 4. Interval data are ordered data for which differences between the numbers make sense, but there is no natural 0 (best example I can come up with is temperature -- the temperature that we call "0 degrees" is arbitrary). Ratio data are like interval data, but they have a natural 0 -- things like heights, weights, etc. Most of the data you'll see is ratio data. Use the Pearson correlation coefficient for this. If the question has the word "rank" or "rating" or "non-parametric", then use the Spearman correlation coefficient.
This week we are working on correlation and regression.
All work that can be done in SPSS must be submitted in that format.
1. Dr. Allen suspects a strong correlation between math anxiety and performance in statistics. To test that hypothesis he collects the following data.
Math Anxiety 1st Exam Score
78
68
82
56
23
22
34
20
53
65
30 42
58
38
75
82
85
49
86
54
53
84
a. Conduct and interpret the appropriate analysis to determine if there is a relationship between math anxiety and performance in statistics.
There are several ways to do this. You could go to analyze  correlate  bivariate to find the correlation, you could go to analyze  regression  linear to do a regression analysis, or you could go to analyze  general linear model  univariate to do a more complicated regression analysis. I'll show you results from the first two. For the regression analysis, you need to choose an ...
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