Wk 7

Ch 13 Problem 63

Refer to the Baseball 2016 data, which reports information on the 2016 Major League Baseball season. Let attendance be the dependent variable and total team salary, in millions of dollars, be the independent variable. Determine the regression equation and answer the following questions.

a. Draw a scatter diagram. From the diagram, does there seem to be a direct relationship between the two variables?

b. What is the expected attendance for a team with a salary of $80.0 million?

c. If the owners pay an additional $30 million, how many more people could they expect to attend?

d. At the .05 significance level, can we conclude that the slope of the regression line is positive? Conduct the appropriate test of hypothesis.

e. What percentage of the variation in attendance is accounted for by salary?

f. Determine the correlation between attendance and team batting average and between attendance and team ERA. Which is stronger? Conduct an appropriate test of hypothesis for each set of variables.

Problem 64

Refer to the Lincolnville School bus data. Develop a regression equation that expresses the relationship between age of the bus and maintenance cost. The age of the bus is the independent variable.

A. Draw a scatter diagram. What does this diagram suggest as to the relationship between the two variables? Is it direct or indirect? Does it appear to be strong or weak?

B. Develop a regression equation. How much does an additional year add to the maintenance cost? What is the estimated maintenance cost for a 10-year-old bus?

C. Conduct a test of hypothesis to determine whether the slope of the regression line is greater than zero. Use the .05 significance level. Interpret your finding from parts a,b, and c in a brief report.

Problem 35

Refer to the Lincolnville School district data. First, add a variable to change the type of engine (diesel or gas) to a qualitive variable. If the engine type is diesel, then set the qualitive variable to 0. If the engine type is gasoline, then set the qualitative variable to 1. Develop a regression equation using statistical software with maintenance cost as the dependent variable and age, odometer miles, miles since last maintenance, and engine type as the independent variables.

a. Develop a correlation matrix. Which independent variables have strong or weak correlations with the dependent variable? Do you see any problems with multicollinearity?

b. Use a statistical software package to determine the multiple regression equation. How did you select the variables to include in the equation? How did you use the information from the correlation analysis? Show that your regression equation shows a significant relationship. Write out the regression equation and interrupt its practical application. Report and interrupt R-square.

c. Develop a histogram or a stem-and-leaf display of the residuals from the final regression equation developed in part (a,b) for residuals analysis. Is it reasonable to conclude that the normality assumption has been met?

d. Plot the residuals against the fitted values from the final regression equation developed in part (c) against the fitted values of Y. Plot the residuals on the vertical axis and the fit-ted values on the horizontal axis.

Case A

Refer the Century Bank data. Using checking account balance as the dependent variable and using as independent variable the number of ATM transactions, the number of other services used, whether the individual has a debit card, and whether interest is paid on the particular account, write a report indicating which of the variables seem related to the account balance and how well they explain the variation in account balance. Should all of the independent variables proposed be used in the analysis or can some be dropped?