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Answer :
Final answer:
The linear correlation coefficient (r) signifies the strength and direction of the relationship between two variables. Values of r near -1, +1, and 0 correspond to strong negative, strong positive, and negligible correlations, respectively. For given r values of -1, -0.992, and -0.049, the corresponding scatter diagrams would illustrate strong negative, nearly perfect negative, and almost zero correlation, respectively.
Explanation:
The subject of this question pertains to the matching of the linear correlation coefficient (r) to the appropriate scatter diagram. The linear correlation coefficient is a statistical measure that calculates the strength of the linear relationship between two variables, represented by the x and y axes on a scatter plot.
Ranging between -1 to +1, it tells us about both the strength and direction of the relationship. A value close to -1 signifies a strong negative correlation, a value close to +1 indicates a strong positive correlation, and a value near zero implies no correlation.
In this specific case, the scatter diagram corresponding to r=-1 demonstrates a strong negative correlation where y decreases as x increases. Scatter diagram for r=-0.992 would show a nearly perfect negative linear relationship while r=-0.049 would visualise an almost negligible correlation between the variables.
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