Question [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
The least squares regression line minimizes the sum of the ____
 A differences between actual and predicted y values B absolute deviations between actual and predicted y values C absolute deviations between actual and predicted x values D squared differences between actual and predicted y values
Explanation:

Detailed explanation-1: -The main objective of the regression analysis is to find the line of best fit that minimizes the sum of the squares of the residuals. In other words, its goal is to minimize the sum of the squared differences of the actual and the predicted value of the dependent variable.

Detailed explanation-2: -The Least Squares Regression Line is the line that minimizes the sum of the residuals squared. In other words, for any other line other than the LSRL, the sum of the residuals squared will be greater. This is what makes the LSRL the sole best-fitting line.

Detailed explanation-3: -The Least Squares Regression Line is the line that makes the vertical distance from the data points to the regression line as small as possible. It’s called a “least squares” because the best line of fit is one that minimizes the variance (the sum of squares of the errors).

Detailed explanation-4: -This method is called the least-squares computation procedure because it aims to minimize the squared distances between each of the points and the line. Least Squares Regression Line (LSRL): The line that minimizes the sum of the squares of the vertical distances of the data points from the line.

Detailed explanation-5: -Properties of the Regression Line The line minimizes the sum of squared differences between observed values (the y values) and predicted values (the ŷ values computed from the regression equation). The regression line passes through the mean of the x values (x) and through the mean of the y values (y).

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