Final answer:
The statement is false; WLS is used when the variance of Y given X is not constant, employing weights to correct for the non-constant variance.
Step-by-step explanation:
The statement 'Weighted Least Squares (WLS) assumes that the variance of the dependent variable (Y) given the values of the independent variables (X) is constant' is false. Ordinary Least Squares (OLS) assumes constant variance, known as homoscedasticity. However, the Weighted Least Squares (WLS) technique is used precisely when the variance of the dependent variable is not constant. In WLS, weights are applied to the observations to correct for heteroscedasticity, or the presence of non-constant variance of the dependent variable's errors given the independent variables.
For clarification, the assumptions of the classical linear regression model include linearity, independence, and normally distributed errors with equal variance (homoscedasticity). WLS is useful when the errors have non-constant variance (heteroscedasticity), allowing for a more efficient estimation of the regression coefficients. The goal is to minimize the weighted sum of squared errors and achieve a best-fit line that compensates for the varying spread of data points around the regression line. This approach typically yields a more accurate estimation of the relationship between the independent and dependent variables when variance is not constant.