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Feature of Least Square regression lines are——— The sum of the deviations at the Y’s or the X’s from their regression lines are zero.
- a)true
- b)false
- c)both
- d)none
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Feature of Least Square regression lines are The sum of the deviations...
Explanation:
The least squares regression line is the line of best fit for a set of data. It is the line that minimizes the sum of the squares of the vertical deviations from the line. The following are the features of the least square regression line:
Sum of deviations:
The sum of the deviations at the Ys or the Xs from their regression lines are zero. This means that the sum of the differences between the actual Y values and the predicted Y values is equal to zero.
Minimizes the sum of squares:
The least squares regression line minimizes the sum of the squares of the vertical deviations from the line. This means that the sum of the squared differences between the actual Y values and the predicted Y values is minimized.
Best fit line:
The least squares regression line is the line of best fit for a set of data. It is the line that best represents the relationship between the X and Y variables.
Linear relationship:
The least squares regression line assumes that there is a linear relationship between the X and Y variables. This means that the relationship between the two variables can be represented by a straight line.
Equal variances:
The least squares regression line assumes that the variances of the Y values are equal for all values of X. This means that the spread of the Y values around the regression line is the same for all values of X.
Independent variables:
The least squares regression line assumes that the X values are independent of each other. This means that the value of one X does not depend on the value of another X.
Therefore, the statement "The sum of the deviations at the Ys or the Xs from their regression lines are zero" is true.
The least squares regression line is the line of best fit for a set of data. It is the line that minimizes the sum of the squares of the vertical deviations from the line. The following are the features of the least square regression line:
Sum of deviations:
The sum of the deviations at the Ys or the Xs from their regression lines are zero. This means that the sum of the differences between the actual Y values and the predicted Y values is equal to zero.
Minimizes the sum of squares:
The least squares regression line minimizes the sum of the squares of the vertical deviations from the line. This means that the sum of the squared differences between the actual Y values and the predicted Y values is minimized.
Best fit line:
The least squares regression line is the line of best fit for a set of data. It is the line that best represents the relationship between the X and Y variables.
Linear relationship:
The least squares regression line assumes that there is a linear relationship between the X and Y variables. This means that the relationship between the two variables can be represented by a straight line.
Equal variances:
The least squares regression line assumes that the variances of the Y values are equal for all values of X. This means that the spread of the Y values around the regression line is the same for all values of X.
Independent variables:
The least squares regression line assumes that the X values are independent of each other. This means that the value of one X does not depend on the value of another X.
Therefore, the statement "The sum of the deviations at the Ys or the Xs from their regression lines are zero" is true.
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Feature of Least Square regression lines are The sum of the deviations at the Ys or the Xs from their regression lines are zero.a)trueb)falsec)bothd)noneCorrect answer is option 'A'. Can you explain this answer?
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