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Chapter 3: Q.2.1 (page 171)

To determine the least-squares regression line:

Short Answer

Expert verified

The regression equation is y^=16.3+0.0908x

Step by step solution

01

Given Information

Given in the question that a data set. We need to determine the least-squares regression line

Body weight (lb)
Backpack weight (lb)
170
26
187
30
109
26
103
24
131
29
165
35
158
31
116
28
02

Explanation

Assume x is Bodyweight and yis Backpack weight.

Find the regression line using the steps provided on theTi-83calculator:

1. Click on STAT > Edit.

2. Enter the data set in L1and L2.

L13. Again, press STAT > CALC >LinReg (ax+b).

4. Press Enter.

The obtained output is: y^=16.3+0.0908x

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Most popular questions from this chapter

Outsourcing by airlines Airlines have increasingly outsourced the maintenance of their planes to other companies. Critics say that the maintenance may be less carefully done, so that outsourcing creates a safety hazard. As evidence, they point to government data on percent of major maintenance outsourced and percent of flight delays blamed on the airline (often due to maintenance problems): Make a scatterplot by hand that shows how delays relate to outsourcing.

(a) Describe the direction, form, and strength of the relationship between maintenance outsourcing and delays blamed on the airline.

(b) One airline is a high outlier in delay percent. Which airline is this? Aside from the outlier, does the plot show a roughly linear form? Is the relationship very strong?

Dem bones Archaeopteryx is an extinct beast having feathers like a bird but teeth and a long bony tail like a reptile. Only six fossil specimens are known. Because these specimens differ greatly in size, some scientists think they are different species rather than individuals from the same species. We will examine some data. If the specimens belong to the same species and differ in size because some are younger than others, there should be a positive linear relationship between the lengths of a pair of bones from all individuals. An outlier from this relationship would suggest a different species. Here are data on the lengths in centimeters of the femur (a leg bone) and the humerus (a bone in the upper arm) for the five specimens that preserve both bones:8

(a) How would rchange if the bones had been measured in millimeters instead of centimeters? (There are 10millimeters in a centimeter.)

(b) If the x and y variables are reversed, how would the correlation change? Explain.

Correlation blunders Each of the following statements contains an error. Explain what’s wrong in each case.

(a) “There is a high correlation between the gender of American workers and their income.”

(b) “We found a high correlation (r=1.09) between students’ ratings of faculty teaching and ratings made by other faculty members.”

(c) “The correlation between planting rate and yield of corn was found to be r=0.23 bushel.”

How much gas? In Exercise 4(page 158), we examined the relationship between the average monthly temperature and the amount of natural gas consumed in Joan’s midwestern home. The figure below shows the original scatterplot with the least-squares line added. The equation of the least-squares line isy^=1425−19.87x

(a) Identify the slope of the line and explain what it means in this setting.

(b) Identify the y-intercept of the line. Explain why it’s risky to use this value as a prediction.

(c) Use the regression line to predict the amount of natural gas Joan will use in a month with an average temperature of 30°F.

Measurements on young children in Mumbai, India, found this least-squares line for predicting height yfrom the arm span x y⏜=6.4+0.93xMeasurements are in centimeters (cm).

One child in the Mumbai study had a height of 59cmand an arm span60cmThis child’s residual is

(a)−3.2cm.(c)−1.3cm.(e)62.2cm.(b)−2.2cm.(d)3.2cm.
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