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Chapter 3: Q 71. (page 209)

Which of the following is not a characteristic of the least-squares regression line?

a. The slope of the least-squares regression line is always between 鈥�1 and 1.

b. The least-squares regression line always goes through the point (x炉,y炉) .

c. The least-squares regression line minimizes the sum of squared residuals.

d. The slope of the least-squares regression line will always have the same sign as the correlation.

e. The least-squares regression line is not resistant to outliers.

Short Answer

Expert verified

The correct option is (a) The slope of the least-squares regression line is always between-1 and 1

Step by step solution

01

Given information

The properties of the least square regression line can be seen in five different ways.

02

Explanation

The equation of the regression line is:

y铃�=a+bxa=y-interceptb=Slopecoefficient

line's values are not limited in any way. It might be positive or negative and have any value. As a result, the slope of the regression line cannot be considered to be between -1and 1

Thus, option (a) is not the characteristic of the regression line.

Hence, the correct option is (a).

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