Answer :
The linear correlation coefficient in a scatter diagram provides a numerical measure of the strength and direction of the linear relationship between two variables. By analyzing the scatter diagram and considering the correlation coefficient, we can determine the nature and strength of the correlation.
In a scatter diagram, the linear correlation coefficient measures the strength and direction of the linear relationship between two variables. It quantifies the degree to which the data points in the scatter diagram cluster around a straight line. The correlation coefficient, often denoted as "r," ranges from -1 to +1.Here are some examples of how the linear correlation coefficient can be matched to the scatter diagram:
1. If the scatter diagram shows a clear upward trend where the data points are tightly clustered around a rising line, then the linear correlation coefficient would be close to +1. This indicates a strong positive correlation between the variables.
2. If the scatter diagram has data points that are widely scattered and do not follow any discernible pattern, the linear correlation coefficient would be close to 0. This suggests a weak or no correlation between the variables.
3. In the case where the scatter diagram shows a clear downward trend where the data points are tightly clustered around a declining line, the linear correlation coefficient would be close to -1. This indicates a strong negative correlation between the variables.
It is important to note that the magnitude of the correlation coefficient (how close it is to 1 or -1) indicates the strength of the correlation, while the sign (+ or -) indicates the direction. The closer the correlation coefficient is to 0, the weaker the correlation.Remember, the linear correlation coefficient only measures linear relationships and does not imply causation. Additionally, it is always important to interpret the scatter diagram in conjunction with the correlation coefficient to draw accurate conclusions about the relationship between the variables.
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