Embed Size (px)
DESCRIPTION
For class practice
Citation preview
Practice Problems: Correlation and Linear Regression
Question 1:
Death Anxiety Religiosity38 442 329 1131 528 915 624 1417 919 1011 158 19
19 173 10
14 146 18
1. What is your computed answer?r = -.696069034 or -.70
3. What percent of the variability is accounted for by the relation of these two variables?
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:
2. What does this statistic mean concerning the relationship between death anxiety and religiosity?
There is a moderate to strong correlation between death anxiety and religiousity. Individuals with high levels of religiosity have lower levels of death anxiety and vice versa. We can not say that participation in religious activities causes lower levels of death anxiety as one can not draw this sort of cause and effect conclusion based on a correlational study.
r2 = .48
Practice Problems: Correlation and Linear Regression Question 2
Achievement GPA98 3.696 2.794 3.188 491 3.277 386 3.871 2.659 363 2.284 1.779 3.175 2.672 2.986 2.485 3.471 2.893 3.790 3.262 1.6
1. Compute the correlation coefficient. r = .524127623 or .52
3. What percent of the variability is accounted for by the relation of these two variables?
4. What would be the slope and y-intercept for a regression line based on this data?The slope would be .028430629 and the y-intercept would be .62711903.
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.
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
2. What does this statistic mean concerning the relationship between death anxiety and
2. What does this statistic mean concerning the relationship between achievement test performance and g.p.a.?There is a moderate to strong correlation between death anxiety and religiousity. Individuals
with high levels of religiosity have lower levels of death anxiety and vice versa. We can not say that participation in religious activities causes lower levels of death anxiety as one can not draw this sort of cause and effect conclusion based on a correlational study.
There is a moderate correlation between achievement test performance and g.p.a. As the achievement test scores go up, the g.p.a.s tend to increase as well and vice versa.
3. What percent of the variability is accounted for by the relationship between the two variables and what does this statistic mean?
r2 = .27 The percent a variability is relatively low. Only 27 percent of the achievement test performance is related to the g.p.a (and vice versa). Seventy-three percent of the variability is left unexplained.
5. If a student scored a 93 on the achievement test, what would be their predicted G.P.A.? 3.27 If they scored a 74? 2.73 A 88? 3.13
Question 3
Dollars Satisfaction11 618 817 1015 49 95 6
12 319 522 225 10
1. Compute the correlation coefficient.r = .076445809 or .08
r = .524127623 or .52
4. What would be the slope and y-intercept for a regression line based on this data?The slope would be .028430629 and the y-intercept would be .62711903.
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.
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.
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?
There is pretty much no relationship between amount of money one spends for a internet service provider and the degree 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?
r2 = .0058 Less than one percent of the variability is explained. This highlights the lack of relationship between the two variables.2. What does this statistic mean concerning the relationship between achievement test
There is a moderate correlation between achievement test performance and g.p.a. As the achievement test scores go up, the g.p.a.s tend to increase as well and vice versa.
3. What percent of the variability is accounted for by the relationship between the two
= .27 The percent a variability is relatively low. Only 27 percent of the achievement test performance is related to the g.p.a (and vice versa). Seventy-three percent of the
5. If a student scored a 93 on the achievement test, what would be their predicted G.P.A.?
Question 4
MHPG Affect980 22
1209 261403 81950 101814 51280 191073 261066 12880 23776 28
1. Compute the correlation coefficient.
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.
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.
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.
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?
There is pretty much no relationship between amount of money one spends for a internet service provider and the degree of customer satisfaction. 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 and what does this statistic mean?
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.
= .0058 Less than one percent of the variability is explained. This highlights the lack of relationship between the two variables.
3. What percent of the variability is accounted for by the relationship between the two variables?
r2 = .61
5. What would be the predicted affect score if the individual had an MHPG level of 1100? of 950? of 700?
1100: 20.34950: 22.9700: 27.17
1. Compute the correlation coefficient. r = -.779443711 or -.78
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.
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.
2. What does this statistic mean concerning the relationship between MHPG levels
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
5. What would be the predicted affect score if the individual had an MHPG level of 1100? of 950? of 700?
