6. Which of the following best describes the difference between the interpretati

Question

6. Which of the following best describes the difference between the interpretation of the corretation coefficient and the beta coefficient for a regression equation expressing the relationship between variables X and Y? A. The beta coefficient represents the linear relationship between X and Y, whereas the correlation 8. The beta coefficient represents the difference between observed and expected values of v c. The beta coefficient predicts increases or decreases in Y with increases or decreases in X, whereas the D. T coefficient represents the percent variability in Y explained by X correlation coefficient represents the linear relationship between X and Y correlation coefficient provides a unit-free measure of the strength of the relationship , whereas the he correlation coefficient predicts increases or decreases in Y with increases or decreases in X, whereas the beta coefficient provides a unit-free measure of the strength of the relationship.

Explanation / Answer

Let us consider a simple linear regression equation as

Y=2+3X

where Y= dependent variable depends on independent variable X.

Here, 3 is beta coefficient of the regression equation or it is sometimes called regression coefficient. Now it indicates that as X increases by one unit then Y is also increased by 3 units and if X is decreased by one unit then Y is also decreased by 3 units.

If the regression equation is

Y=2-3X

Then here the beta coefficient (-3) indicates that as X increases by one unit then Y is also decreased by 3 units and if X is decreased by one unit then Y is also increased by 3 units.

That is, the beta coefficient represents the rate of change of one variable (y) as a function of changes in the other variable (x).

Therefore, beta coefficient predicts increase or decrease in Y with increase or decreases in X.

Now, the correlation coefficient is the degree of relationship between two variables. That is, it gives the degree of relation between X and Y.

Therefore, the correlation coefficient provides a unit free measure of the strength of the relationship.

Therefore option C is correct.

That is, the beta coefficient predicts increase or decreases in Y with increase or decrease in X, whereas the correlation coefficient provides a unit-free measure of the strength of the relationship.

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