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Chapter 3: Q 7. (page 171)

More heavy backpacks Refer to your graph from Exercise 3 Describe the relationship between body weight and backpack weight for this group of hikers.

Short Answer

Expert verified

Linear, positive, and moderately strong association with one outlier.

Step by step solution

01

Given information

For scatterplot:

On horizontal axis: Bodyweight

On vertical axis: Backpack weight

02

Explanation

Strength: The spots in the scatterplot aren't too close together and aren't too far apart either. As a result, strength will be moderate.

Form: There is no substantial curvature in the scatterplot. As a result, the shape will be linear.

Direction: The pattern's upward slope means the direction will be positive.

Unusual features: The rightmost point in the scatterplot appears to vary greatly from the general linear trend seen in the other points. As a result, there is one outlier.

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Most popular questions from this chapter

What鈥檚 my grade? In Professor Friedman鈥檚 economics course, the correlation

between the students鈥� total scores prior to the final examination and their final exam scores is r = 0.6. The pre-exam totals for all students in the course have a mean of 280 and a standard deviation of 30. The final exam scores have a mean of 75 and a standard deviation of 8. Professor Friedman has lost Julie鈥檚 final exam but knows that her total before the exam was 300. He decides to predict her final exam score from her pre-exam total.

a. Find the equation for the least-squares regression line Professor Friedman should use to make this prediction.

b. Use the least-squares regression line to predict Julie鈥檚 final exam score.

c. Explain the meaning of the phrase 鈥渓east squares鈥� in the context of this question.

d. Julie doesn鈥檛 think this method accurately predicts how well she did on the final exam. Determine r2. Use this result to argue that her actual score could have been much higher (or much lower) than the predicted value.

Will I bomb the final? We expect that students who do well on the midterm exam in a course will usually also do well on the final exam. Gary Smith of Pomona College looked at the exam scores of all 346 students who took his statistics class over a 10-year period. 17 The least-squares line for predicting final-exam score from midterm-exam score was y铃�=46.6+0.41x . Octavio scores 10 points above the class mean on the midterm. How many points above the class mean do you predict that he will score on the final? (This is an example of the phenomenon that gave 鈥渞egression鈥� its name: students who do well on the midterm will on the average do less well, but still above average, on the final.)

Windy city Is it possible to use temperature to predict wind speed? Here is a scatterplot showing the average temperature (in degrees Fahrenheit) and average wind speed (in miles per hour) for 365 consecutive days at O鈥橦are International Airport in Chicago.14 Is r>0 or r<0? Closer to r=0orr=卤1? Explain your reasoning.

Actual consumption Refer to Exercise 48. Use the equation of the least-squares regression line and the residual plot to estimate the actual fuel consumption of the car when driving 20 kilometers per hour.

Dem bones Archaeopteryx is an extinct beast that had feathers like a bird but teeth and a long bony tail like a reptile. Only six fossil specimens are known to exist today. Because these specimens differ greatly in size, some scientists think they are different species rather than individuals from the same species. 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:

a. Make a scatterplot. Do you think that all five specimens come from the same species? Explain.

b. Find the correlation r step by step, using the formula on page 166. Explain how your value for r matches your graph in part (a).
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