11. Correlation

What does it mean to say two variables are positively associated? Negatively associated?

True or False: Correlation implies causation.

"[DATA] Influential Observations Zillow.com is a site that can be used to assess the value of homes in your neighborhood. The organization provides a list of homes for sale as well as a Zestimate, which is the price Zillow believes the home will sell for. The following data represent the Zestimate and sale price (in thousands of dollars) of a random sample of recently sold homes in Charleston, South Carolina.

a. Draw a scatter diagram of the data, treating the Zestimate as the explanatory variable and sale price as the response variable."

Suppose you work a part-time job and earn \$15 per hour. Draw a scatter diagram that might represent the relation between your gross pay and hours worked. Is this a deterministic relation or a probabilistic relation?

Finding the Best Model

In Exercises 5–16, construct a scatterplot and identify the mathematical model that best fits the given data. Assume that the model is to be used only for the scope of the given data, and consider only linear, quadratic, logarithmic, exponential, and power models.

Deaths from Motor Vehicle Crashes Listed below are the numbers of deaths in the United States resulting from motor vehicle crashes. Use the best model to find the projected number of such deaths for the year 2025.

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 “Airport Data Speeds,” the P-value is 0.003.

Interpreting r

In Exercises 5–8, use a significance level of α = 0.05 and refer to the accompanying displays.

Bear Length and Weight The lengths (inches) and weights (pounds) of 54 bears are obtained from Data Set 18 “Bear Measurements” in Appendix B, and results are shown in the accompanying XLSTAT display. Is there sufficient evidence to support the claim that there is a linear correlation between length and weight?

Randomization

For Exercises 33–36, repeat the indicated exercise using the resampling method of randomization.

Powerball Jackpots and Tickets Sold Exercise 14