High School

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When examining a scatter diagram, the ________ scattered the points are distributed, the ________ the correlation?

1) less; lower
2) more; lower
3) more; higher
4) less; higher

Answer :

Final answer:

The more scattered the points are on a scatter plot, the lower the correlation between the two variables. This is because a less clustered distribution of points indicates less of a linear relationship and thus a lower correlation coefficient.

Explanation:

When examining a scatter diagram, the more scattered the points are distributed, the lower the correlation. The correct answer to the student's question is option 2) more; lower.

In a scatter plot, a linear relationship between two variables is depicted by points that lie close to a straight line. If there is a positive correlation, the points will form a pattern from the bottom left to the upper right corner with an r value greater than zero. Conversely, if there is a negative correlation, the points will form a pattern from the upper left to the bottom right corner with an r value less than zero. However, when points are randomly distributed with no clear pattern, this suggests a very low or no correlation, meaning an r value of around zero.

It's important to note that the correlation coefficient, denoted as r, quantifies the strength and direction of a linear relationship between two variables. The value of r ranges from -1 (perfect negative correlation) to +1 (perfect positive correlation), with values close to 0 indicating a weak or no linear relationship.

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