The least squared regression minimizes the:
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A. B. C. D.D
The least squared regression minimizes the square of the distance between the observed points and the regression line.
In least squares regression, the goal is to find the best-fitting line that minimizes the sum of the squared differences between the observed data points and the predicted values on the regression line. This method is called "least squares" because it minimizes the sum of the squared residuals, which are the differences between the observed values and the predicted values.
The correct answer is D. The least squared regression minimizes the square of the distance between the observed points and the regression line. This means that it minimizes the sum of the squared residuals. The residuals are the differences between the observed values and the predicted values on the regression line. By squaring these residuals and summing them up, the least squares regression finds the line that minimizes this sum and provides the best overall fit to the data.
Option A, adjusted R-square, is not correct. Adjusted R-square is a measure of the proportion of the variance in the dependent variable that is explained by the independent variables in the regression model. It is a goodness-of-fit measure but not directly related to the minimization process in least squares regression.
Option B, the absolute value of the distance between the observed points and the regression line, is also incorrect. Least squares regression specifically minimizes the sum of the squared residuals, not the absolute values of the residuals.
Option C, explained variance, is not the main objective of least squares regression. Explained variance refers to the proportion of the total variance in the dependent variable that is explained by the independent variables in the regression model. While least squares regression aims to provide a good fit to the data, it does not directly minimize the explained variance.
Therefore, the correct answer is D, the square of the distance between the observed points and the regression line.