## Practice Problems: Correlation and Linear Regression

Researchers interested in determining if there is a relationship between death anxiety and religiosity conducted the following study. Subjects completed a death anxiety scale (high score = high anxiety) and also completed a checklist designed to measure an individuals degree of religiosity (belief in a particular religion, regular attendance at religious services, number of times per week they regularly pray, etc.) (high score = greater religiosity . A data sample is provided below:

 Death Anxiety Religiosity 38 4 42 3 29 11 31 5 28 9 15 6 24 14 17 9 19 10 11 15 8 19 19 17 3 10 14 14 6 18

2. What does this statistic mean concerning the relationship between death anxiety and religiosity?

3. What percent of the variability is accounted for by the relation of these two variables?

It is assumed that achievement test scores should be correlated with student's classroom performance. One would expect that students who consistently perform well in the classroom (tests, quizes, etc.) would also perform well on a standardized achievement test (0 - 100 with 100 indicating high achievement). A teacher decides to examine this hypothesis. At the end of the academic year, she computes a correlation between the students achievement test scores (she purposefully did not look at this data until after she submitted students grades) and the overall g.p.a. for each student computed over the entire year. The data for her class are provided below.

 Achievement G.P.A. 98 3.6 96 2.7 94 3.1 88 4.0 91 3.2 77 3.0 86 3.8 71 2.6 59 3.0 63 2.2 84 1.7 79 3.1 75 2.6 72 2.9 86 2.4 85 3.4 71 2.8 93 3.7 90 3.2 62 1.6

1. Compute the correlation coefficient.

2. What does this statistic mean concerning the relationship between achievement test prformance and g.p.a.?

3. What percent of the variability is accounted for by the relationship between the two variables and what does this statistic mean?

4. What would be the slope and y-intercept for a regression line based on this data?

5. If a student scored a 93 on the achievement test, what would be their predicted G.P.A.? If they scored a 74? A 88?

With the growth of internet service providers, a researcher decides to examine whether there is a correlation between cost of internet service per month (rounded to the nearest dollar) and degree of customer satisfaction (on a scale of 1 - 10 with a 1 being not at all satisfied and a 10 being extremely satisfied). The researcher only includes programs with comparable types of services. A sample of the data is provided below.

 dollars satisfaction 11 6 18 8 17 10 15 4 9 9 5 6 12 3 19 5 22 2 25 10
1. Compute the correlation coefficient.

2. What does this statistic mean concerning the relationship between amount of money spent per month on internet provider service and level of customer satisfaction?

3. What percent of the variability is accounted for by the relationship between the two variables and what does this statistic mean?

It is hypothesized that there are fluctuations in norepinephrine (NE) levels which accompany fluctuations in affect with bipolar affective disorder (manic-depressive illness). Thus, during depressive states, NE levels drop; during manic states, NE levels increase. To test this relationship, researchers measured the level of NE by measuring the metabolite 3-methoxy-4-hydroxyphenylglycol (MHPG in micro gram per 24 hour) in the patient's urine experiencing varying levels of mania/depression. Increased levels of MHPG are correlated with increased metabolism (thus higher levels) of central nervous system NE. Levels of mania/depression were also recorded on a scale with a low score indicating increased mania and a high score increased depression. The data is provided below.

 MHPG Affect 980 22 1209 26 1403 8 1950 10 1814 5 1280 19 1073 26 1066 12 880 23 776 28
1. Compute the correlation coefficient.

2. What does this statistic mean concerning the relationship between MHPG levels and affect?

3. What percent of the variability is accounted for by the relationship between the two variables?

4. What would be the slope and y-intercept for a regression line based on this data?

5. What would be the predicted affect score if the individual had an MHPG level of 1100? of 950? of 700?