Choose a TRUE statement on the linear regression and correlation coefficient. A.
ID: 3326623 • Letter: C
Question
Choose a TRUE statement on the linear regression and correlation coefficient.
A.) The correlation coefficient is the proportion of "variation" in Y that is explained by the independant variable X.
B.) If the coefficient of correlation is -0.90, the coeffiicent of determination is -0.81.
C.) The strength of the correlation between two variables depends on the sign of the coefficient of correlation.
D.) High correlation between X and Y is an indication of their casual relationship.
E.) The correlation coefficient r between X and Y always has the same sign as b in Y = a + bX
Explanation / Answer
Ans:- E
As coefficient of determination is the proportion of variation in Y that is explained by the independent variable X.
If coefficient of correlation is 0.90, the coefficient of determination is +0.81
Strength of the correlation between variable does not depend on the sign of r. As r=+1 or r=-1 both indicate stron correlation.
A correlation between two variables does not imply causation. Even Strong correlation does not imply causation.
When the slope of the regression line is positive i.e. b is positive, the value of y increases as the value of x increases. Therefore positive correlation. And when the slope of the regression line is negative i.e. b is negative, the value of y decreases as x increases. Therefore negative correlation.