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Chapter 4: Problem 2

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

Short Answer

Expert verified
a. Negative correlation. b. Correlation close to 0. c. Positive correlation. d. Positive correlation.

Step by step solution

01

Analyze the relationship between interest rates and number of loan applications

Higher interest rates may deter individuals from applying for loans due to the increased cost of borrowing. As such, one could expect a negative correlation between these two variables.
02

Assess the relationship between height and IQ

Height and IQ are, generally speaking, not directly related. The height of an individual does not determine their intelligence, therefore one could expect a correlation close to 0.
03

Analyze the relationship between height and shoe size

Typically, taller individuals tend to have larger shoe sizes due to proportional body growth. Therefore, a positive correlation can be expected between these two variables
04

Evaluate the relationship between minimum daily temperature and cooling cost

As the minimum daily temperature increases, the need for cooling (via air conditioning for example) also increases, leading to higher cooling costs. As such, one would expect a positive correlation between these two variables.

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Most popular questions from this chapter

An article on the cost of housing in California (San Luis Obispo Tribune, March 30,2001 ) included the following statement: "In Northern California, people from the San Francisco Bay area pushed into the Central Valley, benefiting from home prices that dropped on average \(\$ 4000\) for every mile traveled east of the Bay." If this statement is correct, what is the slope of the least squares regression line, \(\hat{y}=a+b x,\) where \(y=\) house price (in dollars) and \(x=\) distance east of the Bay (in miles)? Justify your answer.

Briefly explain why a large value of \(r^{2}\) is desirable in a regression setting.

The article "Examined Life: What Stanley H. Kaplan Taught Us About the SAT" (The New Yorker [December 17, 2001]: \(86-92\) ) included a summary of findings regarding the use of SAT I scores, SAT II scores, and high school grade point average (GPA) to predict first-year college GPA. The article states that "among these, SAT II scores are the best predictor, explaining 16 percent of the variance in first-year college grades. GPA was second at 15.4 percent, and SAT I was last at 13.3 percent." a. If the data from this study were used to fit a least squares regression line with \(y=\) first-year college GPA and \(x=\) high school GPA, what would be the value of \(r^{2} ?\) b. The article stated that SAT II was the best predictor of first-year college grades. Do you think that predictions based on a least-squares line with \(y=\) first-year college GPA and \(x=\) SAT II score would be very accurate? Explain why or why not.

For a given data set, the sum of squared deviations from the line \(y=40+6 x\) is \(529.5 .\) For this same data set, which of the following could be the sum of squared deviations from the least squares regression line? Explain your choice. i. 308.6 ii. 529.6 iii. 617.4

The article "That's Rich: More You Drink, More You Earn" (Calgary Herald, April 16, 2002) reported that there was a positive correlation between alcohol consumption and income. Is it reasonable to conclude that increasing alcohol consumption will increase income? Explain why or why not.
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