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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 –1 and 1.

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

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⏜=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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Most popular questions from this chapter

The scatterplot shows reading test scores against IQ test scores for 14 fifth-grade children. There is one low outlier in the plot. What effect does this low outlier have on the correlation?

a. It makes the correlation closer to 1.

b. It makes the correlation closer to 0 but still positive.

c. It makes the correlation equal to 0.

d. It makes the correlation negative.

e. It has no effect on the correlation.

More crying? Refer to Exercise 16Does the fact that r=0.45 suggest that making an infant cry will increase his or her IQ later in life? Explain your reasoning.

Teaching and research A college newspaper interviews a psychologist about student ratings of the teaching of faculty members. The psychologist says, “The evidence indicates that the correlation between the research productivity and teaching rating of faculty members is close to zero.” The paper reports this as “Professor McDaniel said that good researchers tend to be poor teachers, and vice versa.” Explain why the paper’s report is wrong. Write a statement in plain language (don’t use the word correlation) to explain the psychologist’s meaning.

Less gas? Refer to Exercise 38.

a. Interpret the slope of the regression line.

b. Does the value of the y intercept have meaning in this context? If so, interpret the y intercept. If not, explain why.

Do muscles burn energy? Metabolic rate, the rate at which the body consumes energy, is important in studies of weight gain, dieting, and exercise. We have data on the lean body mass and resting metabolic rate of 12 women who are subjects in a study on dieting. Lean body mass, given in kilograms, is a person’s weight leaving out all fat. Metabolic rate is measured in calories burned per 24 hours. The researchers believe that lean body mass is an

important influence on metabolic rate.

a. Make a scatterplot to display the relationship between lean body mass and metabolic rate.

b. Describe the relationship between lean body mass and metabolic rate.
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