Question

Multicollinearity exists when the dependent variable and the independent variable are highly correlated. Do you agree? Explain.

1) No. Multicollinearity exists when two or more independent variables are highly correlated with each other.
2) No. Multicollinearity increases the standard errors of the coefficients of the dependent variables, leaving the independent variables highly correlated.
3) Yes. Multicollinearity exists when the dependent variable and the independent variable are highly correlated with each other, resulting in a coefficient of correlation between variables greater than 0.70.
4) Yes. Multicollinearity exists when the dependent variable and the independent variable are highly correlated with each other, resulting in a coefficient of correlation between variables less than 0.70.

Answer 1

Multicollinearity refers to the condition in a regression analysis where two or more independent variables are highly correlated with each other, not with the dependent variable. This can increase standard errors and affect the reliability of statistical inferences within the model.

Step-by-step explanation:

No, multicollinearity does not exist when the dependent variable and the independent variable are highly correlated. Instead, multicollinearity occurs when two or more independent variables in a regression model are highly correlated with each other. This means that the independent variables carry similar information and it becomes difficult for the model to determine the individual effect of each independent variable on the dependent variable.

The number portion of the correlation coefficient indicates the strength of the relationship between two variables. It is a value between -1 and +1, where numbers closer to 1 or -1 signify a stronger linear relationship, and numbers closer to 0 indicate a weaker relationship. If the correlation coefficient is 0, it suggests no linear relationship between the variables.

A high degree of multicollinearity can increase the standard errors of the coefficients, leading to less reliable statistical inferences. It is important to note that multicollinearity deals solely with the relationships between independent variables within the model and not with the dependent variable.