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The linear correlation coefficient measures the strength and direction of the linear relationship between two variables.
The linear correlation coefficient, also known as the correlation coefficient or r-value, measures the strength and direction of the linear relationship between two variables. It ranges from -1 to +1, with -1 indicating a perfect negative linear relationship, +1 indicating a perfect positive linear relationship, and 0 indicating no linear relationship. To match the linear correlation coefficient to the scatter diagram, you can examine the trend in the scatter plot. If the points in the scatter plot form a clear linear pattern, the linear correlation coefficient will be close to -1 or +1. If there is no clear linear pattern, the linear correlation coefficient will be close to 0.
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SOLUTION:
Case: Identifying graphs with corresponding correlation coefficients
Given: Three correlation coefficients with their corresponding graphs
Required: To match the graphs with their correct approximate linear correlation coefficients.
Method: The linear coefficients of graph is evaluated from the level of noise from the line of best fit(the red lines in the image below)
Correlation varies as
1 meaning perfectly correlated
as it tends to zero poor correlation AND
as it tends to one it is a good correlation
From the image above
A matches with (I). No noise
B matches with (II) least noise
C matches with (III) less noise
Final answer:
A) r =0.787. matches with (I)
B) r= 0.946 matches with (II)
C) r=1 matches with (III)
