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Chapter 3: Q 60. (page 193)

Oil and residuals Refer to Exercise 59. The following figure shows a residual plot for the least-squares regression line. Discuss what the residual plot tells

Short Answer

Expert verified

The regression line is not a good fit for the data.

Step by step solution

01

Part (a) Step 1: Given information

02

Part (a) Step 2: Concept

A regression line is a straight line that depicts the change in a response variable y when an explanatory variable x changes. By putting this x into the equation of the line, you may use a regression line to predict the value of y for any value of x

03

Explanation

The anticipated laboratory value from the least-squares line is within -20and +20for the majority of the residuals in the exhibited image. As the laboratory measurement (X)grows, the residual plot shows an increasing spread around the regression line. For larger values of Xpredictions of Yusing this line will be less accurate.

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Most popular questions from this chapter

How much gas? Refer to Exercise 40. During March, the average temperature was 46.4°F and Joan used 490 cubic feet of gas per day. Find and interpret the residual for this month.

Do heavier people burn more energy? Refer to Exercises 54and 56For the regression you performed earlier, r2=0.768 and s=95.08 Explain what each of these values means in this setting.

Do heavier people burn more 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 for 12women who are subjects in a study of dieting. Lean body mass, given in kilograms, is a person’s weight leaving out all fat. Metabolic rate is measured in calories burned per 24hours. The researchers believe that lean body mass is an important influence on metabolic rate.

(a) Make a scatterplot on your calculator to examine the researchers’ belief.

(b) Describe the direction, form, and strength of the relationship.

Measurements on young children in Mumbai, India, found this least-squares line for predicting height y from the arm span x: y⏜=6.4+0.93x

Measurements are in centimeters (cm).

How much does height increase on average for each additional centimeter of arm span?

(a)0.93cm(c)5.81cm(e)7.33cm(b)1.08cm(d)6.4cm

For this regression, s=2.27. Interpret this value in context.
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