Choose a true statement on the linear regression and correlation coefficient. A.
ID: 3303480 • 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 independent variable X.
B.) If the coefficient of correlation is -0.90, the coefficient 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 causal relationship.
E.) The correlation coefficient r between X and Y always has the same sign as b in Y = a+bX
Explanation / Answer
Variation in dependent variable explained by the independent variable is given by the coefficient of determination R2 not by the correlation coefficient. therefore a is also incorrect
The coefficient of determination is computed as the square of the coefficient of correlation. Therefore if the coefficient of correlation is -0.9, then the coefficient of determination would be (-0.9)2 = 0.81 therefore b is also incorrect
The strength of the correlation coefficient depends on the magnitude of the correlation coefficient not on the sign of the correlation coefficient. Therefore c is incorrect
E is the correct answer as a positive correlation coefficient means that the dependent variable value increases with independent variable value and visa versa therefore the slope coefficient would also be positive. Similar reasoning for the negative sign case.