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Questions and Answers
Questions and Answers
What does the correlation coefficient measure?
What does the correlation coefficient measure?
- The difference between two variables
- The product of two variables
- The linear relationship between two variables (correct)
- The average of two variables
Which formula correctly represents the correlation coefficient?
Which formula correctly represents the correlation coefficient?
- $r(x,y) = rac{Cov(x,y)}{ ext{std}(x) imes ext{std}(y)}$ (correct)
- $r(x,y) = rac{Cov(x,y)}{ ext{var}(x) + ext{var}(y)}$
- $r(x,y) = Cov(x,y) imes rac{ ho_x ho_y}{n}$
- $r(x,y) = rac{Cov(x,y)}{ rac{ar{x}}{ar{y}}}$
What effect does a dense clustering of data points have on the correlation coefficient?
What effect does a dense clustering of data points have on the correlation coefficient?
- Eliminates correlation entirely
- Suggests a strong correlation (correct)
- Indicates a weak correlation
- Indicates a perfect correlation
Why might the correlation coefficient not be suitable for very large populations?
Why might the correlation coefficient not be suitable for very large populations?
Which of the following is necessary to calculate the covariance between two variables?
Which of the following is necessary to calculate the covariance between two variables?
Questions and Answers
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Flashcards
Flashcards
Correlation Coefficient Formula
Correlation Coefficient Formula
The correlation coefficient (r) measures the linear relationship between two variables (x and y). It's calculated by dividing the covariance of x and y by the product of their standard deviations.
Correlation Coefficient Meaning
Correlation Coefficient Meaning
A correlation coefficient (r) measures the strength and direction of a linear relationship between two variables. Values close to ±1 indicate a strong linear relationship, while values close to 0 indicate a weak or no linear relationship.
Covariance
Covariance
Covariance measures how two variables change together. A positive covariance suggests that they tend to increase or decrease together. A negative covariance suggests that one variable tends to increase when the other decreases.
Standard Deviation
Standard Deviation
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Correlation Coefficient Interpretation
Correlation Coefficient Interpretation
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Study Notes
Study Notes
Correlation Coefficient
- Correlation measures the linear relationship between two variables.
- If points are close together, there's a strong correlation.
- If points are scattered, there's a weak correlation.
- Karl Pearson developed the correlation coefficient.
- It's denoted by 'r(x,y)'.
- It's a numerical measure of linear relationship.
- The coefficient is a ratio of covariance divided by the standard deviations.
Covariance
- Covariance measures the direction of the relationship between two variables.
- Positive covariance indicates a positive relationship where both variables tend to increase or decrease together.
- Negative covariance indicates a negative relationship where one variable tends to increase as the other decreases.
- The covariance between two variables 'x' and 'y' is denoted by Cov(x,y).
Bivariate Distribution
- It refers to a joint distribution of two variables.
- 'xi, yi (i = 1,2...n)' represents a bivariate distribution.
Calculation of Correlation Coefficient
- r(x,y) = Cov(x,y) / (σx * σy)
- σx = √[(1/n) * Σ(xi - x̄)²]
- σy = √[(1/n) * Σ(yi - ȳ)²]
- Where:
- x̄ = mean of x values
- ȳ = mean of y values
- n = the number of data points
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