Suppose for each student in a statistics class, you record how far he/she sits from the teacher during a particular class session and his/her score on that day’s quiz.
(No explanations are necessary for the following questions.)
a. Students who sit closer to the teacher tend to score higher on the quiz. Would you expect the correlation coefficient between distance and quiz score to be positive, negative, or close to zero?
b. The correlation coefficient between distance and quiz score turns out to be close to 1. Would that prove that sitting close to the teacher causes higher quiz scores?
c. There is really no association between distance and quiz score. Would you expect the correlation coefficient to be positive, negative, or close to zero?
d. There is really no association between distance and quiz score. Is it still possible to calculate a correlation coefficient?
(No explanations are necessary for the following questions.)
a. Students who sit closer to the teacher tend to score higher on the quiz. Would you expect the correlation coefficient between distance and quiz score to be positive, negative, or close to zero?
b. The correlation coefficient between distance and quiz score turns out to be close to 1. Would that prove that sitting close to the teacher causes higher quiz scores?
c. There is really no association between distance and quiz score. Would you expect the correlation coefficient to be positive, negative, or close to zero?
d. There is really no association between distance and quiz score. Is it still possible to calculate a correlation coefficient?
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a) Assuming that how far the student sits from the teacher is recorded as a distance, then the smaller the distance, the greater the quiz score should be, so this would be a negative correlation.
b) +1 means that it is a perfect positive correlation. This would mean that the greater the distance from the teacher, the greater the test score, therefore it would not prove sitting close to the teacher caused higher quiz scores.
c) You would expect it to be close to 0, as there is no correlation (From 0 to +1 would indicate a positive correlation, and from 0 to -1 would indicate a negative correlation, where the larger the number the strong the correlation)
d) Not too sure about the answer to this one, sorry!
You might find it easier to understand if you draw a scatter graph with the 2 variables (in this case distance and test score) along the axis. Then you can plot a few points that agrees with the statement and you should be able to tell by the line if it is positive or negative :)
Hope that helps!
b) +1 means that it is a perfect positive correlation. This would mean that the greater the distance from the teacher, the greater the test score, therefore it would not prove sitting close to the teacher caused higher quiz scores.
c) You would expect it to be close to 0, as there is no correlation (From 0 to +1 would indicate a positive correlation, and from 0 to -1 would indicate a negative correlation, where the larger the number the strong the correlation)
d) Not too sure about the answer to this one, sorry!
You might find it easier to understand if you draw a scatter graph with the 2 variables (in this case distance and test score) along the axis. Then you can plot a few points that agrees with the statement and you should be able to tell by the line if it is positive or negative :)
Hope that helps!