he two regression lines become identical if the correlation coefficient is
Question
he two regression lines become identical if the correlation coefficient is
Solution 1
The two regression lines become identical if the correlation coefficient is either +1 or -1.
Here's the step by step explanation:
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Regression lines are statistical calculations that can be used to predict the value of one variable based on the value of another.
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The correlation coefficient, denoted as r, measures the strength and direction of a linear relationship between two variables. It ranges from -1 to 1.
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If the correlation coefficient is +1, it means that there is a perfect positive linear relationship between the two variables. As one variable increases, the other variable also increases. The regression lines in this case would be identical and slope upwards.
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If the correlation coefficient is -1, it means that there is a perfect negative linear relationship between the two variables. As one variable increases, the other variable decreases. The regression lines in this case would be identical and slope downwards.
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In any other case, when the correlation coefficient is between -1 and +1, the two regression lines would not be identical. They would show some variation depending on the strength and direction of the relationship between the two variables.
Solution 2
The two regression lines become identical if the correlation coefficient is either +1 or -1.
Here's the step by step explanation:
-
Regression lines are statistical calculations that can be used to predict the value of one variable based on the value of another.
-
The correlation coefficient, denoted as r, measures the strength and direction of a linear relationship between two variables. It ranges from -1 to 1.
-
If the correlation coefficient is +1, it means there is a perfect positive linear relationship between the two variables. In this case, the regression lines would be identical because as one variable increases, the other also increases at a consistent rate.
-
If the correlation coefficient is -1, it means there is a perfect negative linear relationship between the two variables. In this case, the regression lines would also be identical because as one variable increases, the other decreases at a consistent rate.
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In any other case (when the correlation coefficient is between -1 and +1), the two regression lines would not be identical. This is because the relationship between the two variables is not perfectly linear.
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