12. Regression

Using the data and results from Problem 2, complete the following:

c. Interpret the slope and y-intercept, if applicable.

You Explain It! CO2 and Energy Production

The least-squares regression equation ŷ = 1.3491x - 11.2847 relates the carbon dioxide emissions (in millions of tonnes), y, and electricity produced (terawatt-hours), x, for all countries in the world.

Source: www.bp.com

a. Interpret the slope.

[DATA] Graduation Rates Go to www.pearsonhighered.com/sullivanstats to obtain the data file 4_2_28 using the file format of your choice for the version of the text you are using. The variable “Cost” represents the four-year cost including tuition, supplies, room and board. The variable “Annual ROI” represents the return on investment for graduates of the school. It essentially represents how much you would earn on the investment of attending the school. The variable “Grad Rate” represents the graduation rate of the school.  

e. Interpret the slope

Problems 17–22 use the results from Problems 27–32 in Section 4.1.

[DATA] Home Runs (Refer to Problem 31, Section 4.1.) The following data represent the speed at which a ball was hit (in miles per hour) and the distance it traveled (in feet) for a random sample of home runs in a Major League baseball game.

b. Explain the meanings of the slope and y-intercept in this context, if appropriate.

Problems 17–22 use the results from Problems 27–32 in Section 4.1.

[DATA] Hurricanes (Refer to Problem 32, Section 4.1.) The following data represent the maximum wind speed (in knots) and atmospheric pressure (in millibars) for a random sample of hurricanes that originated in the Atlantic Ocean.

b. Explain what the slope represents.

Problems 17–22 use the results from Problems 27–32 in Section 4.1.

[DATA] American Black Bears (Refer to Problem 30, Section 4.1.) 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 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 data below represent the lengths of 12 American black bears.

b. Explain the significance of the slope and y-intercept in this situation, if applicable.

Analyzing a Newspaper ArticleA Chicago Tribune article claimed that school districts with higher poverty levels have shorter school days.

b. The least-squares regression line for length, y, and income, x, is y^=−0.0102x+7.11. Explain the meaning of the slope for this regression line. Should the y-intercept be interpreted? If it makes sense, interpret it.