?Estimating r For each of the following, estimate the value of the linear correlation

Linear Correlation In this section we use r to denote the value of the linear correlation coefficient. Why do we refer to this correlation coefficient as being linear?

Causation A study has shown that there is a correlation between body weight and blood pressure. Higher body weights are associated with higher blood pressure levels. Can we conclude that gaining weight is a cause of increased blood pressure?

Scatterplot What is a scatterplot and how does it help us?

Estimating r For each of the following, estimate the value of the linear correlation coefficient r for the given paired data obtained from 50 randomly selected adults. a. Their heights are measured in inches (x) and those same heights are recorded in centimeters (y). b. Their IQ scores (x) are measured and their heights (y) are measured in centimeters. c. Their pulse rates (x) are measured and their IQ scores are measured (y). d. Their heights (x) are measured in centimeters and those same heights are listed again, but with negative signs (y) preceding each of these second listings.

Scatterplot. In Exercises 5–8, use the sample data to construct a scatterplot. Use the first variable for the x-axis. Based on the scatterplot, what do you conclude about a linear correlation? Brain Volume and IQ The table lists brain volumes (\(\mathrm{cm}^{3}\)) and IQ scores of five males (from Data Set 8 “IQ and Brain Size” in Appendix B). Text Transcription: cm^3

Scatterplot. In Exercises 5–8, use the sample data to construct a scatterplot. Use the first variable for the x-axis. Based on the scatterplot, what do you conclude about a linear correlation? Bear Measurements The table lists chest sizes (distance around chest in inches) and weights (pounds) of anesthetized bears that were measured (from Data Set 9 “Bear Measurements” in Appendix B).

Scatterplot. In Exercises 5–8, use the sample data to construct a scatterplot. Use the first variable for the x-axis. Based on the scatterplot, what do you conclude about a linear correlation? Car Weight and Fuel Consumption The table lists weights (pounds) and highway fuel consumption amounts (mpg) for a Hyundai Elantra, Nissan Altima, VW Passat, Buick Lucerne, Mercury Grand Marquis, Honda Civic, and Honda Accord.

Scatterplot. In Exercises 5–8, use the sample data to construct a scatterplot. Use the first variable for the x-axis. Based on the scatterplot, what do you conclude about a linear correlation? Heights of Fathers and Sons The table lists heights (in.) of fathers and the heights (in.) of their first sons (from Francis Galton).

Linear Correlation Coefficient In Exercises 9–12, the linear correlation coefficient r is provided. Use Table 2-11 on page 71 to find the critical values of r. Based on a comparison of the linear correlation coefficient r and the critical values, what do you conclude about a linear correlation? Using the data from Exercise 5 “Brain Volume and IQ,” the linear correlation coefficient is r = 0.127.

Linear Correlation Coefficient In Exercises 9–12, the linear correlation coefficient r is provided. Use Table 2-11 on page 71 to find the critical values of r. Based on a comparison of the linear correlation coefficient r and the critical values, what do you conclude about a linear correlation? Using the data from Exercise 6 “Bear Measurements,” the linear correlation coefficient is r = 0.980.

P-Values In Exercises 13–16, write a statement that interprets the P-value and includes a conclusion about linear correlation. Using the data from Exercise 5 “Brain Volume and IQ,” the P-value is 0.839.

P-Values In Exercises 13–16, write a statement that interprets the P-value and includes a conclusion about linear correlation. Using the data from Exercise 6 “Bear Measurements,” the P-value is 0.000.

Linear Correlation Coefficient In Exercises 9-12, the linear correlation coefficient r is provided. Use Table 2-11 on page 71 to find the critical values of r. Based on a comparison of the linear correlation coefficient r and the critical values, what do you conclude about a linear correlation? Using the data from Exercise 7 “Car Weight and Fuel Consumption,” the linear correlation coefficient is r = -0.987.

Linear Correlation Coefficient In Exercises 9-12, the linear correlation coefficient r is provided. Use Table 2-11 on page 71 to find the critical values of r. Based on a comparison of the linear correlation coefficient r and the critical values, what do you conclude about a linear correlation? Using the data from Exercise 8 “Heights of Fathers and Sons,” the linear correlation coefficient is r = -0.017.

P-Values In Exercises 13–16, write a statement that interprets the P-value and includes a conclusion about linear correlation. Using the data from Exercise 7 “Car Weight and Fuel Consumption,” the P-value is 0.000.

P-Values In Exercises 13–16, write a statement that interprets the P-value and includes a conclusion about linear correlation. Using the data from Exercise 8 “Heights of Fathers and Sons,” the P-value is 0.963.