Exam 3: Scatterplots and Correlation

When water flows across farm land, some of the soil is washed away, resulting in erosion. An experiment was conducted to investigate the effect of the rate of water flow (in liters per second) on the amount of soil washed away (in kilograms). The data are given in the following table; ? ? Flow rate 0.31 0.85 1.26 2.47 3.75 Eroded soil 0.82 1.95 2.18 3.01 6.07 Use technology to obtain the correlation between flow rate and amount of eroded soil. Rounded to 3 decimal places, what is the correlation coefficient?

A research survey of approximately 13,900 incoming freshmen in U.S. universities and colleges found that the amount of time a student spends drinking alcohol is a strong predictor of that student's GPA, with a negative association observed between the two variables. When making a scatterplot of these data, what should we do?

Consider the following scatterplot of two variables X and Y: What can be concluded from this scatterplot?

Does atmospheric pressure have an impact on plant heights? To study this question, 20 Spartina alterniflora plants were planted at sea level (1 atmosphere), while another 20 Spartina alterniflora plants were grown in a special chamber aboard the International Space Station (ISS) (0 atmospheres). The height of the plants after 3 months was recorded. The goal was to see whether the plant heights (in centimeters) were affected by the atmospheric pressure exerted on the plant. Suppose you make a scatterplot of the data in this study. Which of the following best describes how to format this scatterplot?

A student wonders whether people of similar heights tend to date each other. 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): ? ? Women 66 64 66 65 70 65 Men 72 68 70 68 74 69 Which of the following statements about these data is TRUE?

Does atmospheric pressure have an impact on plant heights? To study this question, 20 Spartina alterniflora plants were planted at sea level (1 atmosphere), while another 20 Spartina alterniflora plants were grown in a special chamber aboard the International Space Station (ISS) (0 atmospheres). The height of the plants after 3 months was recorded. The goal was to see whether the plant heights (in centimeters) were affected by the atmospheric pressure exerted on the plant. What is the explanatory variable in this study?

The volume of oxygen consumed (in liters per minute) while a person is at rest and while he or she is exercising (running on a treadmill) was measured for each of 50 subjects. The goal of this study was to determine whether the volume of oxygen consumed during aerobic exercise can be estimated from the amount consumed at rest. The results are plotted below. What is the explanatory variable in this study?

For which of the following scatterplots would the correlation be close to 1?

Do creative people make better teachers? Ten teachers at a large university were given a creativity test (scores range from 0 to 20, with higher scores indicating greater creativity) and were evaluated regarding teaching performance by students and peers (a score of 100 indicates an average performance, and larger scores indicate better performance). The creativity scores and teaching performance scores are given below. ? ? Creativity score Performance score 9 93 7 89 8 95 13 101 10 102 10 96 9 95 18 111 10 103 14 107 What is the response variable in this study?

Consider the following scatterplot of the weight of newborn babies (in grams) versus their length (in centimeters): What would be a plausible value for the correlation between weight and length?

Bird species from temperate regions must cope with relatively short breeding seasons. A study examined the relationship between blood testosterone level (ng/ml) and the duration of the egg-laying period (months) in temperate bird species. The following scatterplot displays this relationship, after taking the logarithm of each variable: Suppose the measurements were switched so that logarithm of testosterone level was treated as an explanatory variable rather than a response variable. What impact would this switch have on the correlation?

The volume of oxygen consumed (in liters per minute) while a person is at rest and while he or she is exercising (running on a treadmill) was measured for each of 50 subjects. The goal of this study was to determine whether the volume of oxygen consumed during aerobic exercise can be estimated from the amount consumed at rest. The results are plotted below. What is the response variable in this study?

Consider the following scatterplot: What is the best description of the form of the relationship represented in the plot?

The volume of oxygen consumed (in liters per minute) while a person is at rest and while he or she is exercising (running on a treadmill) was measured for each of 50 subjects. The goal of this study was to determine whether the volume of oxygen consumed during aerobic exercise can be estimated from the amount consumed at rest. The results are plotted below. What does this scatterplot suggest about the relationship?

Tail-feather length in birds is sometimes a sexually dimorphic trait. That is, the trait differs substantially for males and for females. Researchers studied the relationship between weight (x) and tail-feather length (y) in a sample of five wild male long-tailed finches. Here are the data: What is the approximate value of the correlation coefficient between weight and tail feather length? weight () tail length () 20.8 82.5 19.1 82.5 15.9 67.0 16.7 70.5 15.7 73.5

The protease activity found in walnuts preserved in buffers of various pHs is listed in the following table: ? ? 4.5 5 6 7 8 9 10 protease activity 0.17 0.245 0.28 0.055 0.02 0 0.025 Which of the following scatterplots is a correct representation of the data?

The 2011 Canadian Census at School project collected data on school-age children. The following scatterplot below the mean wrist circumference of boys according to age: The form of the relationship in this scatterplot might best be described as

Bird species from temperate regions must cope with relatively short breeding seasons. A study examined the relationship between blood testosterone level (ng/ml) and the duration of the egg-laying period (months) in temperate bird species. The following scatterplot displays this relationship, after taking the logarithm of each variable: What does this scatterplot reveal?

Which of the following statements about the correlation coefficient r is TRUE?

Bird species from temperate regions must cope with relatively short breeding seasons. A study examined the relationship between blood testosterone level (ng/ml) and the duration of the egg-laying period (months) in temperate bird species. The following scatterplot displays this relationship, after taking the logarithm of each variable: What would a plausible value be for the correlation between the logarithm of egg-laying duration and the logarithm of testosterone level?