Question 1187776: A social psychologist conducts a study to determine the relationship between religion and self-esteem. Ten eighth graders are randomly selected for the study. Each individual undergoes two tests, one measuring self-esteem and the other religious involvement. For the self-esteem test, the lower the score is, the higher self-esteem is; for the test measuring religious involvement, the higher the score is, the higher religious involvement is . The self-esteem test has a range from 1 to 1 0 and the religious involvement test ranges from 0 to 50. For the purposes of this question, assume both tests are well standardized and of interval scaling. The following data are collected.
Subject Religious Involvement Self-Esteem
1 5 8
2 25 3
3 45 2
4 20 7
5 30 5
6 40 5
7 1 4
8 15 4
9 10 7
10 35 3
a. If a relationship exists such that the more religiously involved one is, the higher actual se lf-esteem is,
would you expect r computed on the provided values to be negative or positive? Explain.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the dats, without the subject identification, is shown below.
Religious Involvement Self-Esteem
5 8
25 3
45 2
20 7
30 5
40 5
1 4
15 4
10 7
35 3
For the self-esteem test, the lower the score is, the higher self-esteem is.
For the test measuring religious involvement, the higher the score is, the higher religious involvement is.
a. If a relationship exists such that the more religiously involved one is, the higher actual self esteem is, would you expect r computed on the provided values to be negative or positive? Explain.
since the higher esteem is associated with a lower score, you would expect the r-score to be negative.
the following graph shows the relationship.
the x-axis tracks the religious involvement score, with the higher score being associated with greater religious involvement.
the y-axis tracks the esteem score, with the lower score being associat4ed with higher self esteem.
from the graph, you can see that, as the value of x increases, the value of y decreases.
this associates higher self esteem with greater religious involvement.
here are the results from my used of the alcula regression calculaltor, which can be found on http://www.alcula.com/calculators/statistics/linear-regression/#gsc.tab=0
the correlation coefficient is negative, as you would expect if higher self esteem was associated positively with religious involvement.
the reason for the negative correlation coefficient is because higher esteem is associated with a lower score, with 10 being the lowest self esteem and 1 being the highest self esteem.
the linear regression formula can be rounded to y = 6.49 - .075x.
the 6.49 is the y-intercept, which is the value of y when the value of x is 0.
the - .075x is the slope, which is the change in the value of y divided by the corresponding change in the value of x.
the regression formula finds a straight line that minimizes the distance between that line and the individual plotted points on the graph.
the distance is the vertical distance from the line, as shown in the following picture.
if you want to learn more about regression analysis, here's one that's pretty good and fairly easy to understand.
https://www.purplemath.com/modules/scattreg3.htm
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