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More predictions Hurricane Katrina's hurricane force winds extended 120 miles from its center. Katrina was a big storm, and that affects how we think about the prediction errors. Suppose we add 120 miles to each error to get an idea of how far from the predicted track we might still find damaging winds. Explain what would happen to the correlation between Prediction Error and Year, and why.

Correlation errors Your economics instructor assigns your class to investigate factors associated with the gross domestic product (GDP) of nations. Each student examines a different factor (such as Life Expectancy, Literacy Rate, etc.) for a few countries and reports to the class. Apparently, some of your classmates do not understand statistics very well because you know several of their conclusions are incorrect. Explain the mistakes in their statements: a. "My very low correlation of -0.772 shows that there is almost no association between \(G D P\) and Infant Mortality Rate." b. "There was a correlation of 0.44 between \(G D P\) and Continent."

A researcher studies children in elementary school and finds a strong positive linear association between height and reading scores. a. Does this mean that taller children are generally better readers? b. What might explain the strong correlation?

Smartphones and life expectancy A survey of the world's nations in 2014 shows a strong positive correlation between percentage of the country using smartphones and life expectancy in years at birth. a. Does this mean that smartphones are good for your health? b. What might explain the strong correlation?

The correlation between Age and Income as measured on 100 people is \(r=0.75\). Explain whether or not each of these possible conclusions is justified: a. When Age increases, Income increases as well. b. The form of the relationship between Age and Income is straight. c. There are no outliers in the scatterplot of Income vs. Age. d. Whether we measure Age in years or months, the correlation will still be 0.75

The correlation between Fuel Efficiency (as measured by miles per gallon) and Price of 150 cars at a large dealership is \(r=-0.34\). Explain whether or not each of these possible conclusions is justified: a. The more you pay, the lower the fuel efficiency of your car will be. b. The form of the relationship between Fuel Efficiency and Price is moderately straight. c. There are several outliers that explain the low correlation. d. If we measure Fuel Efficiency in kilometers per liter instead of miles per gallon, the correlation will increase.

Baldness and heart disease Medical researchers followed 1435 middle-aged men for a period of 5 years, measuring the amount of Baldness present (none \(=1,\) little \(=2,\) some \(=3,\) much \(=4,\) extreme \(=5)\) and presence of Heart Disease \((\mathrm{No}=0, \mathrm{Yes}=1)\). They found a correlation of 0.089 between the two variables. Comment on their conclusion that this shows that baldness is not a possible cause of heart disease.

The Office of Federal Housing Enterprise Oversight (www.fhfa.gov) collects data on various aspects of housing costs around the United States. Here is a scatterplot of the Housing Cost Index versus the Median Family Income for each of the 50 states. The correlation is \(0.65 .\) a) Describe the relationship between the Housing Cost Index and the Median Family Income by state. b) If we standardized both variables, what would the correlation coefficient between the standardized variables be? c) If we had measured Median Family Income in thousands of dollars instead of dollars, how would the correlation change? d) Washington, DC, has a housing cost index of 548 and a median income of about \(\$ 45,000\). If we were to include \(\mathrm{DC}\) in the dataset, how would that affect the correlation coefficient? e) Do these data provide proof that by raising the median family income in a state, the housing cost index will rise as a result? Explain. \({ }^{\star} \mathrm{f}\) ) For these data Kendall's tau is 0.51 . Does that provide proof that by raising the median income in a state, the Housing Cost Index will rise as a result? Explain what Kendall's tau says and does not say.

Interest rates and mortgages 2015 Since 1985 , average mortgage interest rates have fluctuated from a low of nearly \(3 \%\) to a high of over \(14 \%\). Is there a relationship between the amount of money people borrow and the interest rate that's offered? Here is a scatterplot of Mortgage Loan Amount in the United States (in trillions of dollars) versus yearly Interest Rate since 1985 . The correlation is -0.85 . a. Describe the relationship between Mortgage Loan Amount and Interest Rate. b. If we standardized both variables, what would the correlation coefficient between the standardized variables be? c. If we were to measure Mortgage Loan Amount in billions of dollars instead of trillions of dollars, how would the correlation coefficient change? d. Suppose that next year, interest rates were \(11 \%\) and mortgages totaled \(\$ 60\) trillion. How would including that year with these data affect the correlation coefficient? e. Do these data provide proof that if mortgage rates are lowered, people will take out larger mortgages? Explain. f. For these data Kendall's tau is -0.65. Does that provide proof that if mortgage rates are lowered, people will take out more mortgages? Explain what Kendall's tau says and does not say.

American League baseball games are played under the designated hitter rule, meaning that pitchers, often weak hitters, do not come to bat. Baseball owners believe that the designated hitter rule means more runs scored, which in turn means higher attendance. Is there evidence that more fans attend games if the teams score more runs? Data collected from American League games during the 2016 season indicate a correlation of 0.432 between runs scored and the average number of people at the home games. (www.espn.com/mlb/ attendance) a. Does the scatterplot indicate that it's appropriate to calculate a correlation? Explain. b. Describe the association between attendance and runs scored. c. Does this association prove that the owners are right that more fans will come to games if the teams score more runs?