11. Correlation

4. Give examples of two variables that have perfect positive linear correlation and two variables that have perfect negative linear correlation.

In Exercise 23, add data for a child who is 6 years old and has a vocabulary of 900 words. Describe how this affects the correlation coefficient r.

In Exercise 24, remove the data for the student who is 57 inches tall and scored 128 on the IQ test. Describe how this affects the correlation coefficient r.

In Exercise 25, remove the data for the international soccer player with a maximum weight of 170 kilograms and a jump height of 64 centimeters. Describe how this affects the correlation coefficient r.

In Exercise 26, add data for an international soccer player who can perform the half squat with a maximum of 210 kilograms and can sprint 10 meters in 2.00 seconds. Describe how this affects the correlation coefficient r.

The TIMMS Exam The Trends in International Mathematics and Science (TIMMS) is a mathematics and science achievement exam given internationally. On each exam, students are asked to respond to a variety of background questions. For the 41 nations that participated in TIMMS, the correlation between the percentage of items answered in the background questionnaire (used as a proxy for student task persistence) and mean score on the exam was 0.79. Does this suggest there is a linear relation between student task persistence and achievement score? Write a sentence that explains what this result might mean.

In Problems 3–6, use the results in the table to (b) determine the linear correlation between the observed values and expected z-scores, (c) determine the critical value in Table VI to assess the normality of the data.

In Problems 3–6, use the results in the table to (b) determine the linear correlation between the observed values and expected z-scores, (c) determine the critical value in Table VI to assess the normality of the data.

Time and Motion In a physics experiment at Doane College, a soccer ball was thrown upward from the bed of a moving truck. The table below lists the time (sec) that has lapsed from the throw and the corresponding height (m) of the soccer ball.

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a. Find the value of the linear correlation coefficient r.

[DATA] Buying a New Car How much does the typical person pay for a new 2019 Audi A4? The following data represent the selling price of a random sample of new A4s (in dollars).

d. Verify it is reasonable to conclude that this data come from a population that is normally distributed.

Bull Markets A bull market is defined as a market condition in which the price of a security rises for an extended period of time. A bull market in the stock market is often defined as a condition in which a market rises by 20% or more without a 20% decline. The data to the right represent the number of months and percentage change in the S&P 500 (a group of 500 stocks) during the 25 bull markets dating back to 1929 (the year of the famous market crash).

b. Determine the linear correlation coefficient between months and percent change.

Time and Motion In a physics experiment at Doane College, a soccer ball was thrown upward from the bed of a moving truck. The table below lists the time (sec) that has lapsed from the throw and the corresponding height (m) of the soccer ball.

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b. Based on the result from part (a), what do you conclude about a linear correlation between time and height?

[DATA] American Black Bears The American black bear (Ursus americanus) is one of eight bear species in the world. It is the smallest North American bear and the most common bear species on the planet. In 1969, Dr. Michael R. Pelton of the University of Tennessee initiated a long-term study of the population in the Great Smoky Mountains National Park. One aspect of the study was to develop a model that could be used to predict a bear’s weight (since it is not practical to weigh bears in the field). One variable thought to be related to weight is the length of the bear. The following data represent the lengths and weights of 12 American black bears.

c. Determine the linear correlation coefficient between weight and length.

d. Does a linear relation exist between the weight of the bear and its length?

[DATA] Bear Markets A bear market in the stock market is defined as a condition in which the market declines by 20% or more over the course of at least two months. The following data represent the number of months and percentage change in the S&P 500 (a group of 500 stocks) for a sample of bear markets.

b. Determine the linear correlation coefficient between months and percent change.

c. Does a linear relation exist between duration of the bear market and market performance?

[DATA] Draw Your Data! Consider the four data sets shown below.

a. Compute the linear correlation coefficient for each data set.