Which of the following statements is true with respect to a simple linear regression model?
A) The percent of variation in the dependent variable that is explained by the regression model is equal to the square of the correlation coefficient between the x and y variables.
B) If the correlation coefficient between the x and y variables is negative, the sign on the regression slope coefficient will also be negative.
C) If the correlation between the dependent and the independent variable is determined to be significant, the regression model for y given x will also be significant.
D) All of the above are true.

Question

Quizplus · Accepted Answer

A) This statement is true because the coefficient of determination (R^2) is indeed the square of the correlation coefficient (r) between the independent variable (x) and the dependent variable (y), which explains the proportion of the variance in the dependent variable that is predictable from the independent variable. B) This is true because the sign of the correlation coefficient indicates the direction of the relationship between x and y. A negative correlation means that as x increases, y decreases, which is reflected in a negative slope coefficient in the regression equation. C) If the correlation is significant, it implies there is a statistically significant relationship between x and y. While this doesn't guarantee the regression model will be significant in all aspects (e.g., all predictors being significant if multiple regression), it strongly suggests the model explaining y given x has a significant linear component.

Which of the Following Statements Is True with Respect to a Simple