Block 5 Homework Answer Key (2)
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Elon University *
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STS 110
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Feb 20, 2024
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BLOCK 5 HOMEWORK
100 POINTS
DUE TUESDAY, JANUARY 16 at 11:59 PM
Figure 1. Graph of Purity Score on the y-axis and Proportionality Score on the x-axis
Figure 1 is a graph from a sample of Elon University STS 1100 students’ morality survey from Fall Semester 2023. The correlation coefficient was 0.213, r-squared is 0.045, and the equation of the best-fit line in red is Y = 1.25 + 0.29X.
1.
What type of graph is Figure 1? For example, it is not a histogram but a _
scatterplot
__.
2.
What direction is the correlation (positive, negative, or none)?
Positive
(can tell by the slope being positive, the correlation coefficient ( r ) value being positive, and the dots and best-fit line on Figure 1 going up from left to right. 3.
What strength is the correlation (none, weak, moderate, strong, or perfect)?
Weak because if we look at the table for the values of the correlation coefficient in the block 5 slides, this is the appropriate strength. 4.
One group last semester thought that the value of student’s proportionality score caused
the value of their purity score to be what it was, and that the purity score was affected by
the proportionality score. a.
If proportionality score was the cause in the relationship between purity and proportionality, did they put proportionality on the correct axis in Figure 1?
Yes
, because the cause goes on the X (horizontal) axis.
b.
According to Figure 1, which variable did the group think was the response variable?
Purity
because the response variable goes on the Y (vertical axis). We can also look at the paragraph in this question and see that purity was the effect, which goes on the Y-axis.
c.
If the true relationship between proportionality score and purity score was that a person’s overall morality was why both scores are what they are,
which is the best choice for why we see the correlation in Figure 1 and Table 1:
coincidence, common underlying cause, or cause-and-effect? Explain your decision.
Common underlying cause because a common underlying cause affects both the X and Y variables.
Cause-and-effect is a two-variable relationship but here we see morality as a third variable involved. Common underlying cause involves at least one variable other than the X and Y variables in the correlation. If there is a reason for this relationship, as given here in the question 4c, then the
relationship is not a coincidence. 5.
Look at Figure 1. Write the coordinates of what you think is the most extreme outlier. Use the format we learned in class
(1.8, 4.5)
; but I will accept the coordinates of the dots on the upper right side of the graph, as they are also relatively far away from the other dots.
6.
Does the outlier you chose in question 5 increase, decrease, or not change the strength of the correlation?
Decrease the strength
; unless you chose one of the dots near the best-fit line for question 5 (which would be incorrect), the outlier does not strengthen the correlation. It is possible for an outlier to increase the strength of the correlation, but it does not do so here. 7.
One Elon University STS 1100 student from Fall Semester 2023 forgot to add their morality survey data to the Google sheet that the data we see in Table 1 and Figure 1 came from. The student and the statistician would like to add their data to the analysis, but the student only remembers that their proportionality score was 2.6. They do not remember their purity score. Would the statistician be allowed to predict that student’s purity score according to the four conditions (or rules) we learned in class? Explain your answer by explaining whether each of the four rules was met or violated.
No, because the rule requiring strong or perfect correlation was not met since there was a weak correlation. The rule requiring interpolation was met because their proportionality score of 2.6 is between 1.8 and 5, which are the smallest and largest x values we see among the dots on the graph. The rule requiring the same population was met because the population of the graph is Elon University STS 1100 students from Fall Semester 2023 says the description of the graph and correlation below Figure 1. The rule requiring the same time period was met because the time period was Fall Semester 2023 for the correlation and figure 1 and the time period of the student’s data was from Fall Semester 2023.
8.
What is the value of the y-intercept
of the best-fit line in Figure 1?
Use the paragraph of information below Figure 1, as the best-fit line on the graph may not include the y-intercept (this is not unusual).
1.25
because this number is by itself without the X
9.
If purity and proportionality scores could both range from zero to five, what would the value of the y-intercept tell us about purity and proportionality?
It would tell us that when the proportionality score (x) is zero, the purity score (y) would be about 1.25. When describing the y-intercept or slope, you have to say something to indicate that the relationships they describe are estimates that are not always true. Here, you could say “about 1.25”, “approximately 1.25”, “expected to be 1.25”, “on average 1.25”, etc.
10.
What is the value of the slope
of the best-fit line in Figure 1?
Use the paragraph of information below Figure 1 instead of trying to calculate or estimate it from the graph.
0.29 because this number is together with X.
11.
What does the value of the slope tell us about the relationship between the change in purity and the change in proportionality? Use specific numbers in your discussion and talk about both variables: purity and proportionality.
When purity score (y variable) increases by 0.29, we expect the proportionality score to increase by about 1.
Slope is change in y divided by change in x. For a slope of 0.29, this can be expressed in many ways, but the easiest is a change of 0.29 (y) divided by a change of 1 (x). The positive number for the slope tell us that the change in both x and y will be the same
direction (they both increase or both decrease). In my version of the answer, purity and proportionality increase as shown by the fact I use positive numbers. I could also say when purity decreases by 0.29, proportionality decreases by 1, which is the fraction -
0.29 / -1 = 0.29 (a negative number divided by a negative number is a positive number).
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Saying both scores increase or decrease together or that the best-fit line and dots go up from left to right is correct, but not sufficient because the sign of the slope (a positive number) tells us this. The value of the purity score (0.29) tells us something much more specific.
When describing the y-intercept or slope, you have to say something to indicate that the relationships they describe are estimates that are not always true. Here, you could say “about 1”, “approximately 1”, “expected to be 1”, “an average of 1” etc.
12. What proportion of variation in the purity score is explained by the proportionality score? 0.045
because r-squared is a proportion that measures variation in a correlation.