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For a set of bivariate data, Pearson's correlation coefficient is -1 - HSC - SSCE Mathematics Standard - Question 12 - 2020 - Paper 1
Question 12
For a set of bivariate data, Pearson's correlation coefficient is -1. Which graph could best represent this set of bivariate data?
Worked Solution & Example Answer:For a set of bivariate data, Pearson's correlation coefficient is -1 - HSC - SSCE Mathematics Standard - Question 12 - 2020 - Paper 1
Step 1
Identify the key feature of Pearson's correlation coefficient
Answer
Pearson's correlation coefficient (r) measures the strength and direction of a linear relationship between two variables. A coefficient of -1 indicates a perfect negative linear relationship. This means that as one variable increases, the other variable decreases in a perfectly linear manner.
Step 2
Analyze the options provided
Answer
We need to identify the graph where the points form a straight line sloping downwards from left to right, signifying that as x increases, y decreases. From the given options:
- Graph A shows no clear negative relationship.
- Graph B also does not depict a linear relationship.
- Graph C shows a positive relationship and is therefore incorrect.
- Graph D displays a straight line descending from left to right, perfectly representing the negative correlation described.
Step 3