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Chapter 4: Problem 58

For each of the following pairs of variables, indicate whether you would expect a positive correlation, a negative correlation, or a correlation close to \(0 .\) Explain your choice. a. Price and weight of an apple b. A person's height and the number of pets he or she has c. Time spent studying for an exam and score on the exam d. A person's weight and the time it takes him or her to run one mile

Short Answer

Expert verified
a. Positive correlation - Heavier apples generally cost more. b. No correlation - A person's height has nothing to do with how many pets they own. c. Positive correlation - The longer you study, the better you're likely to score. d. Negative correlation - Heavier people generally take longer to run a mile.

Step by step solution

01

Correlation between Price and weight of an apple

Generally, for most goods, there is a positive correlation between weight and price. As the weight of an apple increases, so does the price. This is because you are essentially getting more apple for your purchase.
02

Correlation between a person's height and the number of pets he or she has

There is likely little to no correlation between a person's height and the number of pets they have. These variables are largely unrelated. Your height does not influence or is influenced by the number of pets you have. Therefore, the correlation here would be close to 0.
03

Correlation between Time spent studying for an exam and score on the exam

Generally, there is a positive correlation between the amount of time spent studying for an exam and the score on the exam. More time studying typically leads to better understanding of the material, and thus, a higher score. However, efficiency and quality of studying also play a major role.
04

Correlation between a person's weight and the time it takes him or her to run one mile

Generally, there is a negative correlation between a person's weight and the time it takes to run one mile. The more a person weighs, the slower they may run a mile, given that more weight could make running more physically challenging. However, personal fitness and athleticism also play a role in the time taken.

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Most popular questions from this chapter

Explain why it can be dangerous to use the least squares regression line to obtain predictions for \(x\) values that are substantially larger or smaller than the \(x\) values in the data set.

Data on \(x=\) size of a house (in square feet) and \(y=\) amount of natural gas used (therms) during a specified period were used to fit the least squares regression line. The slope was 0.017 and the intercept was \(-5.0 .\) Houses in this data set ranged in size from 1,000 to 3,000 square feet. a. What is the equation of the least squares regression line? b. What would you predict for gas usage for a 2,100 sq. ft. house? c. What is the approximate change in gas usage associated with a 1 sq. ft. increase in size? d. Would you use the least squares regression line to predict gas usage for a 500 sq. ft. house? Why or why not?

In a study of the relationship between TV viewing and eating habits, a sample of 548 ethnically diverse students from Massachusetts was followed over a 19 -month period (Pediatrics [2003]: 1321-1326). For each additional hour of television viewed per day, the number of fruit and vegetable servings per day was found to decrease on average by 0.14 serving. a. For this study, what is the response variable? What is the predictor variable? b. Would the least squares regression line for predicting number of servings of fruits and vegetables using number of hours spent watching TV have a positive or negative slope? Justify your choice.

The paper "School Achievement Strongly Predicts Midlife IQ" (Intelligence [2007]: \(563-567\) ) examined the relationship between school achievement test scores in grades 3 to 8 and IQ measured many years later. The authors reported an association between school achievement test score and midlife IQ, with a correlation coefficient of \(r=0.64\) a. Interpret the value of the correlation coefficient. b. A science writer commenting on this paper (Livescience, April 16,2007\()\) said that the correlation between school achievement test scores and IQ was very strong - even stronger than the correlation between height and weight in adults. Which of the following values for correlation between height and weight in adults is consistent with this statement? Justify your choice. \(\begin{array}{lllll}r=-0.8 & r=-0.3 & r=0.0 & r=0.6 & r=0.8\end{array}\)

For each of the following pairs of variables, indicate whether you would expect a positive correlation, a negative correlation, or a correlation close to \(0 .\) Explain your choice. a. Interest rate and number of loan applications b. Height and \(\mathrm{IQ}\) c. Height and shoe size d. Minimum daily temperature and cooling cost
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