Question

What is the relationship between the linear correlation coefficient r and the slope of a regression​ line?

Answer 1

Answer:

The relationship is that the value of the linear correlation coefficient will always have the same sign as the value of the slope of a regression​ line.

Step-by-step explanation:

The slope of regression is simply the covariance between X and Y divided by the variance of X i.e Cov(X, Y)/Var X. Whereas, the correlation is the covariance divided by the product of the standard deviation. Thus, we can say that the correlation is the product of the gradient of the regression line and the ratio of the standard deviations.

Thus, it means when the correlation is positive, the slope is also positive and vice versa.

Answer 2

The sign of the correlation coefficient, r, is always the same as that of the slope of the regression line.

Linear Correlation Coefficient and Slope of A Regression Line

• Slope of a regression line is gotten by dividing the covariance of between X and Y by the variance of X.
• On the other hand, linear correlation coefficient is gotten by dividing the covariance by the standard deviation.
• Thus, if the slope of regression line is positive, the correlation coefficient will be positive too and vice versa.

Therefore, the sign of the correlation coefficient, r, is always the same as that of the slope of the regression line.

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