If a scatterplot shows a strong positive linear correlation, then which of the following best describes the trend of the data points?
A) Points in a perfectly straight line that rises from left to right
B) Points in a perfectly straight line that falls from left to right
C) Points that fit fairly close to a straight line that rises from left to right
D) Points that fit fairly close to a straight line that falls from left to right
Answer (2)
To determine the best description of the trend of data points in a scatterplot with a strong positive linear correlation, let's break down what this means.
A strong positive linear correlation indicates that the data points closely follow a straight line, and as one variable increases, the other variable also increases. Now, let's evaluate the choices provided:
A) Points in a perfectly straight line that rises from left to right
This would describe a perfect positive linear correlation, where every point lies exactly on a straight line. In reality, this is quite rare as most data will have some variability.
B) Points in a perfectly straight line that falls from left to right
This describes a perfect negative linear correlation, which is the opposite of a positive correlation.
C) Points that fit fairly close to a straight line that rises from left to right
This describes a strong positive linear correlation well. The points do not have to be perfectly aligned but should lie close to a line that rises.
D) Points that fit fairly close to a straight line that falls from left to right
This describes a strong negative linear correlation, not a positive one.
Based on the explanation, the most accurate description for a strong positive linear correlation is:
C) Points that fit fairly close to a straight line that rises from left to right.
In conclusion, when you have a strong positive linear correlation, the data points in the scatterplot will tend to rise from left to right, following a general linear trend. This trend describes how the variables are positively related, meaning as one variable increases, the other tends to increase as well.
The best description of the trend of data points in a scatterplot with a strong positive linear correlation is that they fit fairly close to a straight line that rises from left to right. Therefore, the chosen option is C. This indicates that as one variable increases, the other variable also tends to increase.
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