Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations. Coefficients Standard Error Constant 12.924 4.425 x1 -3.682 2.630 x2 45.216 12.560 Analysis of Variance Source of Variation Degrees of Freedom Sum of Squares Mean Square F Regression 4853 2426.5 Error 485.3 The t value obtained from the table which is used to test an individual parameter at the 1% level is a. 2.977. b. 2.921. c. 3.012. d. 2.650.

Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations. Coefficients Standard Error Constant 12.924 4.425 x1 -3.682 2.630 x2 45.216 12.560 Analysis of Variance Source of Variation Degrees of Freedom Sum of Squares Mean Square F Regression 4853 2426.5 Error 485.3 The t value obtained from the table which is used to test an individual parameter at the 1% level is a. 2.977. b. 2.921. c. 3.012. d. 2.650.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter13: Regression And Forecasting Models

Section13.4: Multiple Regression Models

Problem 13P: A trucking company wants to predict the yearly maintenance expense (Y) for a truck using the number...

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A small computer chip manufacturer wants to forecast monthly ozperating costs as a function of the number of units produced during a month. The company has collected the 16 months of data in the file P13_34.xlsx. a. Determine an equation that can be used to predict monthly production costs from units produced. Are there any outliers? b. How could the regression line obtained in part a be used to determine whether the company was efficient or inefficient during any particular month?
Suppose that a regional express delivery service company wants to estimate the cost of shipping a package (Y) as a function of cargo type, where cargo type includes the following possibilities: fragile, semifragile, and durable. Costs for 15 randomly chosen packages of approximately the same weight and same distance shipped, but of different cargo types, are provided in the file P13_16.xlsx. a. Estimate a regression equation using the given sample data, and interpret the estimated regression coefficients. b. According to the estimated regression equation, which cargo type is the most costly to ship? Which cargo type is the least costly to ship? c. How well does the estimated equation fit the given sample data? How might the fit be improved? d. Given the estimated regression equation, predict the cost of shipping a package with semifragile cargo.
An antique collector believes that the price received for a particular item increases with its age and with the number of bidders. The file P13_14.xlsx contains data on these three variables for 32 recently auctioned comparable items. Estimate a multiple regression equation using the given data. Interpret each of the estimated regression coefficients. Is the antique collector correct in believing that the price received for the item increases with its age and with the number of bidders? Interpret the standard error of estimate and the R-square value for these data.
The management of a technology company is trying to determine the variable that best explains the variation of employee salaries using a sample of 52 full-time employees; see the file P13_08.xlsx. Estimate simple linear regression equations to identify which of the following has the strongest linear relationship with annual salary: the employees gender, age, number of years of relevant work experience prior to employment at the company, number of years of employment at the company, or number of years of post secondary education. Provide support for your conclusion.
A trucking company wants to predict the yearly maintenance expense (Y) for a truck using the number of miles driven during the year (X1) and the age of the truck (X2, in years) at the beginning of the year. The company has gathered the data given in the file P13_13.xlsx. Note that each observation corresponds to a particular truck. Estimate a multiple regression equation using the given data. Interpret each of the estimated regression coefficients. Also, interpret the standard error of estimate and the R-square value for these data.
The Baker Company wants to develop a budget to predict how overhead costs vary with activity levels. Management is trying to decide whether direct labor hours (DLH) or units produced is the better measure of activity for the firm. Monthly data for the preceding 24 months appear in the file P13_40.xlsx. Use regression analysis to determine which measure, DLH or Units (or both), should be used for the budget. How would the regression equation be used to obtain the budget for the firms overhead costs?
The owner of a restaurant in Bloomington, Indiana, has recorded sales data for the past 19 years. He has also recorded data on potentially relevant variables. The data are listed in the file P13_17.xlsx. a. Estimate a simple regression equation involving annual sales (the dependent variable) and the size of the population residing within 10 miles of the restaurant (the explanatory variable). Interpret R-square for this regression. b. Add another explanatory variableannual advertising expendituresto the regression equation in part a. Estimate and interpret this expanded equation. How does the R-square value for this multiple regression equation compare to that of the simple regression equation estimated in part a? Explain any difference between the two R-square values. How can you use the adjusted R-squares for a comparison of the two equations? c. Add one more explanatory variable to the multiple regression equation estimated in part b. In particular, estimate and interpret the coefficients of a multiple regression equation that includes the previous years advertising expenditure. How does the inclusion of this third explanatory variable affect the R-square, compared to the corresponding values for the equation of part b? Explain any changes in this value. What does the adjusted R-square for the new equation tell you?
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The file P14_01.xlsx contains data on 100 consumers who drink beer. Some of them prefer light beer, and others prefer regular beer. A major beer producer believes that the following variables might be useful in discriminating between these two groups: gender, marital status, annual income level, and age. a. Use logistic regression to classify the consumers on the basis of these explanatory variables. How successful is it? Which variables appear to be most important in the classification? b. Consider a new customer: Male, Married, Income 42,000, Age 47. Use the logistic regression equation to estimate the probability that this customer prefers Regular. How would you classify this person?
Regression analysis is a powerful and commonly used tool in business research. One important step in regression is to determine the dependent and independent variable(s). In a bivariate regression, which variable is the dependent variable and which one is the independent variable? What does the intercept of a regression tell? What does the slope of a regression tell? What are some of the main uses of a regression? Provide an example of a situation wherein a bivariate regression would be a good choice for analyzing data. Justify your answers using examples and reasoning.
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The regression equation of two variables are 5y = 9x - 22 and 20x = 9y + 350Find the means of x and y. Also find the value of r.

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	Coefficients	Standard Error
Constant	12.924	4.425
x₁	-3.682	2.630
x₂	45.216	12.560

Analysis of Variance
Source of Variation	Degrees of Freedom	Sum of Squares	Mean Square	F
Regression		4853	2426.5
Error			485.3