Determine whether each of the following statements is true or false. a. The least-squares regression line is the line that makes the square of the correlation in the data as large as possible. False b. The least-squares regression line is the line that makes the sum of the squares of the vertical distances of the data points from the line as small as possible True c. The least-squares regression line is the line that best splits the data in half, with half of the points above the line and half below the line. False d. The least-squares regression line always passes through the point (x-bar,y-bar ), the means of the explanatory and response variables, respectively. True

Answer:

Options A & C are False while Options B & D are true.

Step-by-step explanation:

The definition of least squares regression line is given as;

The Least Squares Regression Line is a line that normally causes the vertical distance from the data points to the regression line to be as small as possible.

The term “least squares” is derived from the fact that the best line of fit is one that minimizes the the sum of squares of the errors which is also called the variance.

From this definition above, we can see that options A and C are false while option B is the perfect definition for the least line of squares.

Now, the point (x-bar,y-bar ) is known as the mean.

However, every least squares must pass through the middle point of the given data. The mean is the middle point of data in regression analysis. Thus, we can infer that the least-squares regression line always passes through the mean which is point (x-bar,y-bar ). Thus, option D is true.

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