4.24 Data on dating. A student wonders if tall women tend to date taller men than do short women. She measures herself, her dormitory roommate, and the women in the adjoining rooms; then she measures the next man each woman dates. Here are the data (heights in inches)

4.27. The Sanchez household is about to install solar panels to reduce the cost of heating their house. In order to know how much the solar panels will help, they record their consumption of natural gas before the Panels are installed. Gas consumption is higher in cold weather, so the relationship between outside temperature and gas consumption is important. Here are data for 16 consecutive months

Outside temperature is recorded in degree-days, a common measure of demand for heating. A day's degree-days are the number of degrees its average temperature frills below 65 ^o F. Gas used is recorded in hundreds of cubic feet. Make a plot and describe the pattern. Is correlation a helpful way to describe the pattern? Why or why not? Find the correlation if it is helpful.

4.35. Sloppy writing about correlation. Each of the following statements contains a blunder. Explain in each case what is wrong.

1. "There is a high correlation between the gender of American workers and their income."
2. "We found a high correlation r = 1.09 between students' ratings of faculty teaching and ratings made bye other faculty members"
3. "The correlation between planting rate and yield of corn was found to be r = 0.23 bushels"

5.24. Penguins diving. A study of king penguins looked for a relationship between how deep the penguins dive to seek food and how long they stay underwater. For all but the shallowest dives, there is a linear relationship that is different for different penguins. The study report gives a scatterplot for one penguin titled "The relation of dive duration (DD) to depth (D). Duration is measured in minutes, and depth D is in meters. The report then says, "The regression equation for this bird is:

1. What is the slope of the regression line? Explain in specific language what- this slope says about this penguin's dives.
2. According to the regression line, how long does a typical dive to a depth of 200 meters last?
3. The dives varied from 40 meters to 300 meters in depth. Plot the regression line from x = 40 to x = 300.

5.28. Does social rejection hurt? Exercise 4.40 (page 114) gives data from a study that shows that social exclusion causes "real pain". That is, activity in an area of the brain that responds to physical pain goes up as distress from social exclusion goes up. A scatterplot shows a moderately strong linear relationship. Figure 5.10 below shows the regression output from software for these data

1. What is the equation of the least-.squares regression line Cot predicting brain activity from social distress score? Use the equation to predict brain activity for a social distress score 2.0.
2. What percent of the variation in brain activity among these subjects is explained by the straight-line relationship with social distress score?

5.32. Going to class. A study of class attendance and grades among first-year students at a state university showed that in general students who attended a higher percent of their classes earned higher grades. Class attendance explained 16% of the variation in grade index among the students. What is the numerical value of correlation between percent a of class attended and grade index?

6.19. Marital distributions. Give the two marginal distributions for marital status and for job grade. Do each of your raw sets of percents add to exactly 100%? If not, why not?

6.20. Percents. What percent of single men hold Grade 1 jobs? What percent of Grade 1 jobs are held by single men?

6.21. Conditional distribution. Give (in percents) the conditional distribution of job grade among single men. Should your percents add up 100% (up to round off error)?

6.22. Marital status and job grade. One way to see the relationship is to look at who holds Grade 1 jobs.

1. There are 874 married men with Grade 1 jobs, and only 58 single men with such jobs. Explain why these counts by themselves don't describe the relationship between marital status and job grade.
2. Find the percent of men in each marital status group who have Grade 1 jobs. Then find the percent in each marital group who, have Grade 4. What do these percents say about the relationship?

6.23: Association is not causation.. The data in Table 6.4 show that single men are more likely to hold lower-grade jobs than are married men. We should not conclude that single men can help their career by getting married. What lurking variables might help explain the association between marital status on job grade?

6.28. Do angry people have more heart disease? People who get angry easily tend to

have mote heart disease. That's the conclusion of a study that followed a random sample of 12,986 people from three locations for about four years. All subjects were free of heart disease at the beginning of the study. The subjects took the Spielberger Trait Anger Scale test, which measures now prone a person is to sudden anger. Here are data for the 8474 people in the sample who had normal blood pressure. CHD stands for "coronary heart disease". This includes people who had heart attacks and those who needed medical treatment for heart disease.

Do these data support the study's conclusion about the relationship between anger and heart disease?

7.28. Scatterplot. Plot the weight of the bar of soap against day. Is the overall pattern roughly linear? Based on your scatterplot, is, the correlation between day and weight close to 1, positive but not close to 1, close to 0, negative but not close to 1, or close to -1? Explain your answer.

7.29. Regression. Find the equation of the least squares regression line for predicting soap weight from day.

1. What is the equation? Explain what it tells us about the rate at which the soap lost weight.
2. Mr. Boggs did not measure the weight or the soap on day 4. Use the regression equation to predict that weight. .
3. Draw the regression line on your scatterplot from the previous exercise.

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