## Practice Problems: Correlation and Linear Regression Answer

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. r = -.779443711 or -.78

2. What does this statistic mean concerning the relationship between MHPG levels and affect? There is a relatively strong negative correlation between the two variables. As the level of MHPG found in the urine increases, the affect test score decreases (low score represents increased mania) and a lower level of MHPG is associated with higher affect test scores (higher scores associated with depression). It is important to remember that we do not know the direction of the cause (affect -> biochemical changes or biochemical changes -> affect) or whether another variable is involved.

3. What percent of the variability is accounted for by the relationship between the two variables? r2 = .61

4. What would be the slope and y-intercept for a regression line based on this data? The slope would be -.017062474 and the y-intercept would be 39.11036137.

5. What would be the predicted affect score if the individual had an MHPG level of 1100? 20.34; of 950? 22.9; of 700? 27.17

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