BUS352 Chapter 13 Problems

13.3 A small business analyst seeks to determine which variables should be used to predict small-business mean annual revenue for U.S. metropolitan areas. The analyst decides to consider the independent variables age, the mean age (in months) of small businesses in the metropolitan area; and BizAnalyzer, the mean   BizAnalyzer score of small businesses in the metropolitan area. (The BizAnalyzer score measures on a scale of 1 to100 the level of risk that the small businesses in the metropolitan area present to potential lenders.) The dependent variable, revenue, is mean annual   revenue. Using data collected from a sample of 25 metropolitan areas, the regression results are:       

a.  State the multiple regression equation.     

b.  Interpret the meaning of the slopes, b1 and b2, in this problem.   

c.  What conclusions can you reach concerning mean annual revenue?        

13.5 The production of wine is a multibillion-dollar worldwide industry. In an attempt to develop a model of wine quality as judged by wine experts, data was collected from red wine variants of Portuguese “Vinho Verde” wine. A sample of 50 wines is stored in VinhoVerde. (Data extracted from P. Cortez, A.   Cerdeira, F. Almeida, T. Matos, and J. Reis, “Modeling Wine Decision Support Systems, 47, 2009, pp. 547–553 and bit.ly/9xKlEa.) Develop a multiple linear regression model to predict     wine   quality, measured on a scale from 0 (very bad) to 10 (excellent) based on alcohol content (%) and the amount of chlorides.     

a.  State the multiple regression equation.       

b.  Interpret the meaning of the slopes, b1 and b2, in this problem.    

c.  E xplain why the regression coefficient, b0, has no practical meaning in the context of this problem.       

d.  Predict the mean wine quality rating for wines that have 10% alcohol and chlorides of 0.08.        

e.  Construct a 95% confidence interval estimate for the mean wine quality rating for wines that have 10% alcohol and chlorides of 0.08.         

f.   Construct a 95% prediction interval for the wine quality rating for an individual wine that has 10% alcohol and chlorides of 0.08.     

g.  What conclusions can you reach concerning this regression model?