Chapter 14, Problem 14.25CYU

Illustrate the difference between a linear and nonlinear relationship using a graphical presentation and interpret what occurs in the relationships between variables that form the line graph or curve.

What type of variation illustrate the increase or decrease of both variables together?

Southerly Showtime Movie Theaters, Inc. owns and operates a chain of cinemas in several markets in the southern United States. The owners would like to estimate weekly gross revenue as a function of advertising expenditures. Data for a sample of eight markets for a recent week follow. (Let x1 represent Television Advertising ($100s), x2 represent Newspaper Advertising ($100s), and y represent Weekly Gross Revenue ($100s).) Market Weekly Gross Revenue ($100s) Television Advertising ($100s) Newspaper Advertising ($100s) Market 1 101.3 4.9 1.4 Market 2 51.9 2.9 3.1 Market 3 74.8 3.9 1.4 Market 4 126.2 4.4 4.2 Market 5 137.8 3.7 3.9 Market 6 101.4 3.4 2.4 Market 7 237.8 5.1 8.5 Market 8 219.6 7.0 5.7 (a) Develop an estimated linear regression equation with the amount of television advertising as the independent variable. (Round your numerical values to four decimal places.) ŷ =        Test for a significant relationship between the amount spent on television…

If data set has a relationtionship that is best described by a linear model, then the residual plot will

Give 2 characteristics that indicate a linear model may be appropriate to model a data set

The graph shown below represents how the 2011 graduates of law school are doing compared to the 2007 graduates. Both the 2011 and 2007 graduating class had about 44,000 students. 80.0% 70.0% 60.0% 50.0% 40.0% 30.0% 20.0% 10.0% 0.0% 2007 2011 Employment for New Law Grads Class of 2007 vs. Class of 2011 Pt. I (National Association of Legal Placement) Full-Time Lawyer 74.1% 59.8% Full-Time Non- Lawyer 11.8% 14.9% % Part Time 4.1% 10.0% Not Working 5.8% 12.1% (a) What percentage of those Not Working in this study graduated in 2011? Note: 12.1% is not the correct answer. This does require a calculation. Back in School 2.3% 2.2% Report the answer to the nearest tenth of a percent. (b) Show calculations and explain your reasoning for this question.

An important advance in ecological research is the Theory of Island Blogeography, which demonstrates a relationship between the size of islands and the number of species of different amphibians that can be found in the islands, The scatterplot of number of species versus island area (in thousands of square miles) is nonlinear. The graphs below show the results of two different transformations of the data. Model I plots the square of the number of species against area. Model II plots the square root of the number of species against area. Linear regression analyses are provided below. Model II: VNumber of species vs. Area Model I: (Number of Species)? vs. Area 10 8000 9. ecies)

The coefficient of determination measures the percentage of variation in the independent variable explained by the dependent variable. True or  False

Why is is easier to judge if a linear relationship exists between your plotted variable, as opposed to a particular mathematical relationship that is nonlinear?