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Business Statistics For Contemporary Decision Making 8th Edition Black Ken - Solutions
Determine the equation of the least squares regression line to predict y from the following data.a. Construct a 95% confidence interval to estimate the mean y value for x = 60.b. Construct a 95% prediction interval to estimate an individual y value for x = 70.c. Interpret the results obtained in
Determine the equation of the trend line through the following cost data. Use the equation of the line to forecast cost for year 7.Year ... Cost ($ millions)1 ..... 562 ..... 543 ..... 494 ..... 465 ..... 45
A manager of a car dealership believes there is a relationship between the number of salespeople on duty and the number of cars sold. Suppose the following sample is used to develop a simple regression model to predict the number of cars sold by the number of salespeople. Solve for r2 and explain
The American Research Group, Inc. conducted a telephone survey of a random sample of 1, 100 U.S. adults in a recent year and determined that the average amount of planned spending on gifts for the holiday season was $854 and that 40% of the purchases would be made from catalogs. Shown below are the
It seems logical that restaurant chains with more units (restaurants) would have greater sales. This assumption is mitigated, however, by several possibilities: some units may be more profitable than others, some units may be larger, some units may serve more meals, and some units may serve more
Shown here are the labor force figures (in millions) published by Index Mundi for the country of Bangladesh over a 10-year period. Develop the equation of a trend line through these data and use the equation to predict the labor force of Bangladesh for the year 2015.Year ... Labor Force
How strong is the correlation between the inflation rate and 30-year treasury yields? The following data published by Fuji Securities are given as pairs of inflation rates and treasury yields for selected years over a 35-year period.Inflation Rate ..... 30-Year Treasury Yield1.57%
Shown below are data on the total sales generated by the seafood industry and the corresponding jobs supported by the seafood industry in the top 15 states by seafood sales. The data are published by the National Marine Fisheries Service of the National Oceanic and Atmospheric Administration of the
People in the aerospace industry believe the cost of a space project is a function of the weight of the major object being sent into space. Use the following data to develop a regression model to predict the cost of a space project by the weight of the space object. Determine r2 and se. Weight
The following data represent a breakdown of state banks and all savings organizations in the United States every 5 years over a 60-year span, according to the Federal Reserve System.Develop a regression model to predict the total number of state banks by the number of all savings organizations.
Is the amount of money spent by companies on advertising a function of the total revenue of the company? Shown are revenue and advertising cost data for nine companies published by Advertising Age.Use the data to develop a regression line to predict the amount of advertising by revenues. Compute se
Can the consumption of water in a city be predicted by air temperature? The following data represent a sample of a day’s water consumption and the high temperature for that day.Water Use Temperature(Millions of gallons). (Degrees Fahrenheit)219 ......... 103056 ......... 39107 ........
Study the following Minitab output from a regression analysis to predict y from x.a. What is the equation of the regression model?b. What is the meaning of the coefficient of x?c. What is the result of the test of the slope of the regression model? Let α = .10.Why is the t ratio
Study the following Excel regression output for an analysis attempting to predict the number of union members in the United States by the size of the labor force for selected years over a 30-year period from data published by the U.S. Bureau of Labor Statistics. Analyze the computer output. Discuss
Compute r2 for Problem 12.24 (Problem 12.6). Discuss the value of r2 obtained.
Compute r2 for Problem 12.25 (Problem 12.7). Discuss the value of r2 obtained.
Compute r2 for Problem 12.26 (Problem 12.8). Discuss the value of r2 obtained.
Compute r2 for Problem 12.27 (Problem 12.9). Discuss the value of r2 obtained.
In Problem 12.10, you were asked to develop the equation of a regression model to predict the number of business bankruptcies by the number of firm births. For this regression model, solve for the coefficient of determination and comment on it.
Study the following Minitab residual diagnostic graphs. Comment on any possible violations of regressionassumptions.
The Delta Wire Corporation was founded in 1978 in Clarksdale, Mississippi. The company manufactures high-carbon specialty steel wire for global markets and at present employs about 100 people. For the past few years, sales increased each year.A few years ago, however, things did not look as bright
Use a computer to develop the equation of the regression model for the following data. Comment on the regression coefficients. Determine the predicted value of y for x1 = 200 and x2 =7.
Use a computer to develop the equation of the regression model for the following data. Comment on the regression coefficients. Determine the predicted value of y for x1 = 33, x2 = 29, and x3 =13.
Examine the Minitab output shown here for a multiple regression analysis. How many predictors were there in this model? Comment on the overall significance of the regression model. Discuss the t ratios of the variables and theirsignificance.
Using the data from Problem 13.6, develop a multiple regression model to predict insider ownership from debt ratio and dividend payout. Comment on the strength of the model and the predictors by examining the ANOVA table and the ttests.
Study the Minitab output shown in Problem 13.7.Comment on the overall strength of the regression model in light of S, R2, and adjustedR2.
Study the Minitab output shown in Problem 13.8.Comment on the overall strength of the regression model in light of S, R2, and adjustedR2.
Using the regression output obtained by working Problem 13.11, comment on the overall strength of the regression model using S, R2, and adjustedR2.
Study the Minitab residual diagnostic output that follows. Discuss any potential problems with meeting the regression assumptions for this regression analysis based on the residual graphics.
Using the following data determine the equation of the regression model. How many independent variables are there? Comment on the meaning of these regression coefficients.Predictor .. CoefficientConstant ... 121.62x1 ...... -.174x2 ...... 6.02x3 .... .00026x4 .... .0041
Use the following data to determine the equation of the multiple regression model. Comment on the regression coefficients.Predictor .. CoefficientConstant .... 31,409.5x1 ...... .08425x2 ...... 289.62x3 ....... -.0947
Is there a particular product that is an indicator of per capita personal consumption for countries around the world? Shown on the next page are data on per capita personal consumption, paper consumption, fish consumption, and gasoline consumption for 11 countries. Use the data to develop a
Jensen, Solberg, and Zorn investigated the relationship of insider ownership, debt, and dividend policies in companies. One of their findings was that firms with high insider ownership choose lower levels of both debt and dividends. Shown here is a sample of data of these three variables for 11
Displayed here is the Minitab output for a multiple regression analysis. Study the ANOVA table and the t ratios and use these to discuss the strengths of the regression model and the predictors. Does this model appear to fit the data well? From the information here, what recommendations would you
Using the data in Problem 13.5, develop a multiple regression model to predict per capita personal consumption by the consumption of paper, fish, and gasoline. Discuss the output and pay particular attention to the F test and the ttests.
Develop a multiple regression model to predict y from x1, x2, and x3 using the following data. Discuss the values of F andt.
Use the following data to develop a regression model to predict y from x1 and x2. Comment on the output. Develop a regression model to predict y from x1 only. Compare the results of this model with those of the model using both predictors. What might you conclude by examining the output from both
Study the following Excel multiple regression output. How many predictors are in this model? How many observations? What is the equation of the regression line? Discuss the strength of the model in terms F. Which predictors, if any, are significant? Why or why not? Comment on the overall
Using the regression output obtained by working Problem 13.5, comment on the overall strength of the regression model using S, R2, and adjusted R2. Discuss.
Using the regression output obtained by working Problem 13.12, comment on the overall strength of the regression model using S, R2, and adjusted R2. Discuss.
Study the Minitab regression output that follows. How many predictors are there? What is the equation of the regression model? Using the key statistics discussed in this chapter, discuss the strength of the model and thepredictors.
Study the Excel regression output that follows. How many predictors are there? What is the equation of the regression model? Using the key statistics discussed in this chapter, discuss the strength of the model and itspredictors.
Use the following data to develop a multiple regression model to predict y from x1 and x2. Discuss the output, including comments about the overall strength of the model, the significance of the regression coefficients, and other indicators of model fit.
Given here are the data for a dependent variable, y, and independent variables. Use these data to develop a regression model to predict y. Discuss theoutput.
The U.S. Bureau of Mines produces data on the price of minerals. Shown here are the average prices per year for several minerals over a decade. Use these data and multiple regressions to produce a model to predict the average price of gold from the other variables. Comment on the results of
The Shipbuilders Council of America in Washington, D.C., publishes data about private shipyards. Among the variables reported by this organization are the employment figures (per 1000), the number of naval vessels under construction, and the number of repairs or conversions done to commercial ships
The U.S. Bureau of Labor Statistics produces consumer price indexes for several different categories. Shown here are the percentage changes in consumer price indexes over a period of 20 years for food, shelter, apparel, and fuel oil. Also displayed are the percentage changes in consumer price
The U.S. Department of Agriculture publishes data annually on various selected farm products. Shown here are the unit production figures (in millions of bushels) for three farm products for 10 years during a 20-year period. Use these data and multiple regression analysis to predict corn production
The American Chamber of Commerce Researchers Association compiles cost-of-living indexes for selected metropolitan areas. Shown here are cost-of-living indexes for 25 different cities on five different items for a recent year. Use the data to develop a regression model to predict the grocery
Shown here are the data for y and three predictors, x1, x2, and x3.A multiple regression analysis has been done on these data; the Minitab results are given. Comment on the outcome of the analysis in light of thedata.
Minitab residual diagnostic output from the multiple regression analysis for the data given in Problem 13.30 follows. Discuss any potential problems with meeting the regression assumptions for this regression analysis based on the residualgraphics.
Starbucks is a resounding restaurant success story. Beginning with its first coffee house in 1971, Starbucks has grown to more than 11,000 U.S. locations. Opening up its first international outlet in the mid-1990s, Starbucks now operates in more than 50 countries outside of North America. Besides
Use the following data to develop a quadratic model to predict y from x. Develop a simple regression model from the data and compare the results of the two models. Does the quadratic model seem to provide any better predictability? Why or whynot?
Develop a multiple regression model of the formUsing the following data to predict y from x. From a scatter plot and Tukeys ladder of transformation, explore ways to recode the data and develop an alternative regression model. Compare theresults.
The Publishers Information Bureau in New York City released magazine advertising expenditure data compiled by leading national advertisers. The data were organized by product type over several years. Shown here are data on total magazine advertising expenditures and household equipment and supplies
Dun & Bradstreet reports, among other things, information about new business incorporations and number of business failures over several years. Shown here are data on business failures and current liabilities of the failing companies over several years. Use these data and the following model to
Use the following data to develop a curvilinear model to predict y. Include both x1 and x2 in the model in addition to x21 and x22, and the interaction term x1x2. Comment on the overall strength of the model and the significance of each predictor. Develop a regression model with the same
What follows is Excel output from a regression model to predict y using x1, x2, x21, x22, and the interaction term, x1x2. Comment on the overall strength of the model and the significance of each predictor. The data follow the Excel output. Develop a regression model with the same independent
Analyze the following data by using a multiple regression computer software package to predict y using x1 and x2. x2 is a dummy variable. Discuss the output from the regression analysis; in particular, comment on the predictability of the dummyvariable.
Given here are the data from a dependent variable and two independent variables. The second independent variable is an indicator variable with several categories. Hence, this variable is represented by x2, x3, and x4.How many categories are needed in total for this independent variable? Use a
Given here is Excel output for a multiple regression model that was developed to predict y from two independent variables, x1 and x2.Variablex2is a dummy variable. Discuss the strength of the multiple regression models on the basis of the output. Focus on the contribution of the dummy variable.
Falvey, Fried, and Richards developed a multiple regression model to predict the average price of a meal at New Orleans restaurants. The variables explored included such indicator variables as the following: Accepts reservations, Has its own parking lot, Has a separate bar or lounge, Has a maitre
Use a stepwise regression procedure and the following data to develop a multiple regression model to predict y. Discuss the variables that enter at each step, commenting on their t values and on the value ofR2.
Given here are data for a dependent variable and four potential predictors. Use these data and a stepwise regression procedure to develop a multiple regression model to predict y. Examine the values of t and R2 at each step and comment on those values. How many steps did the procedure use? Why do
The computer output given here is the result of a stepwise multiple regression analysis to predict a dependent variable by using six predictor variables. The numbers of observations were 108. Study the output and discuss the results. How many predictors ended up in the model? Which predictors, if
Study the output given here from a stepwise multiple regression analysis to predict y from four variables. Comment on the output at eachstep.
The National Underwriter Company in Cincinnati, Ohio, publishes property and casualty insurance data. Given here is a portion of the data published. These data include information from the U.S. insurance industry about (1) net income after taxes,(2) dividends to policyholders,(3) net underwriting
Develop a correlation matrix for the independent variables in Problem 14.13. Study the matrix and make a judgment as to whether substantial multicollinearity is present among the predictors. Why or whynot?
Construct a correlation matrix for the four independent variables for Problem 14.14 and search for possible multi-co-linearity. What did you find, and why?
In Problem 14.17, you were asked to use stepwise regression to predict premiums earned by net income, dividends, and underwriting gain or loss. Study the stepwise results, including the regression coefficients, to determine whether there may be a problem with multi-co-linearity. Construct a
Study the three predictor variables in Problem 14.18 and attempt to determine whether substantial multicollinearity is present among the predictor variables. If there is a problem of multi-co-linearity, how might it affect the outcome of the multiple regressionanalysis?
The Hospital database associated with this text and found in Wiley PLUS contains a dichotomous variable, Service, that represents two types of hospitals, general medical and psychiatric. In the database, general medical hospitals are coded as 1 and psychiatric hospitals as 2.However, to run a
Another database associated with this text and found in Wiley PLUS is the Consumer Food database. There is a dichotomous variable in this database, and that is whether a family lives in a metro area or outside. In the database, metro is coded as 1 and outside metro as 2. However, to run a logistic
The Manufacturing database associated with this text and found in Wiley PLUS has a variable, Value of Industrial Shipments that is coded 0 if the value is small and 1 if the value is large. Using Minitab, a logistic regression analysis was done in an attempt to predict the value of industrial
Suppose logistic regression is used to develop a second model from the Manufacturing database discussed in problem 14.25 to predict the value of industrial shipments by two variables, Number of Production Workers and New Capital Expenditures. The Minitab output for this analysis is given below.
Given here are the data for a dependent variable, y, and independent variables. Use these data to develop a regression model to predict y. Discuss the output. Which variable is an indicator variable? Was it a significant predictor ofy?
Use the following data and a stepwise regression analysis to predict y. In addition to the two independent variables given here, include three other predictors in your analysis: the square of each x as a predictor and an interaction predictor. Discuss the results of theprocess.
Use the x1 values and the log of the x1values given here to predict the y values by using a stepwise regression procedure. Discuss the output. Was either or both of the predictorssignificant?
The U.S. Commodities Futures Trading Commission reports on the volume of trading in the U.S. commodity futures exchanges. Shown here are the figures for grain, oilseeds, and livestock products over a period of several years. Use these data to develop a multiple regression model to predict grain
The U.S. Bureau of Mines produces data on the price of minerals. Shown here are the average prices per year for several minerals over a decade. Use these data and a stepwise regression procedure to produce a model to predict the average price of gold from the other variables. Comment on the results
The Shipbuilders Council of America in Washington, D.C., publishes data about private shipyards. Among the variables reported by this organization are the employment figures (per 1000), the number of naval vessels under construction, and the number of repairs or conversions done to commercial ships
The U.S. Bureau of Labor Statistics produces consumer price indexes for several different categories. Shown here are the percentage changes in consumer price indexes over a period of 20 years for food, shelter, apparel, and fuel oil. Also displayed are the percentage changes in consumer price
The U.S. Department of Agriculture publishes data annually on various selected farm products. Shown here are the unit production figures for three farm products for 10 years during a 20-year period. Use these data and a stepwise regression analysis to predict corn production by the production of
The American Chamber of Commerce Researchers Association compiles cost-of-living indexes for selected metropolitan areas. Shown here are cost-of-living indexes for 25 different cities on five different items for a recent year. Use the data to develop a regression model to predict the grocery
A stepwise regression procedure was used to analyze a set of 20 observations taken on four predictor variables to predict a dependent variable. The results of this procedure are given next. Discuss the results.
Shown here are the data for y and three predictors, x1, x2, and x3.A stepwise regression procedure has been done on these data; the results are also given. Comment on the outcome of the stepwise analysis in light of thedata.
Shown below is output from two Excel regression analyses on the same problem. The first output was done on a full model. In the second output, the variable with the smallest absolute t value has been removed, and the regression has been rerun as a second step of a backward
Shown below is Minitab output from a logistic regression analysis to develop a model to predict whether a shopper in a mall store will purchase something by the number of miles the shopper drives to get to the mall store. The original data were coded as 1 if the shopper purchases something and 0 if
The Minitab output displayed here is the result of a multiple regression analysis with three independent variables. Variable x1 is a dummy variable. Discuss the computer output and the role x1 plays in this regression model.
The U.S. Energy Information Administration releases figures in their publication, Monthly Energy Review, about the cost of various fuels and electricity. Shown here are the figures for four different items over a 12-year period. Use the data and stepwise regression to predict the cost of
Virginia Semiconductor is a leading manufacturer of prime silicon substrates. The company, situated in Fredericksburg, Virginia, was founded in 1978 by Dr. Thomas G. Digges and his brother, Robert. Virginia Semiconductor (VSI) was growing and prospering in the early 1980s by selling a high volume
Use the forecast errors given here to compute MAD and MSE. Discuss the information yielded by each type of error measurement.Period .... e1 ...... 2.32 ...... 1.63 ..... -1.44 ..... 1.15 .... .36 .... -.97 .... -1.98 .... -2.19 .... .7
Determine the error for each of the following forecasts. Compute MAD andMSE.
Using the following data determine the values of MAD and MSE. Which of these measurements of error seems to yield the best information about the forecasts?Why?
Figures for acres of tomatoes harvested in the United States from an 11-year period follow. The data are published by the U.S. Department of Agriculture. With these data, forecasts have been made by using techniques presented later in this chapter. Compute MAD and MSE on these forecasts. Comment on
Use the following time-series data to answer the given questions.a. Develop forecasts for periods 5 through 10 using 4-month moving averages.b. Develop forecasts for periods 5 through 10 using 4-month weighted moving averages. Weight the most recent month by a factor of 4, the previous month by 2,
Following are time-series data for eight different periods. Use exponential smoothing to forecast the values for periods 3 through 8.Use the value for the first period as the forecast for the second period. Compute forecasts using two different values of alpha, α = .1 and
Following are time-series data for nine time periods. Use exponential smoothing with constants of .3 and .7 to forecast time periods 3 through 9.Let the value for time period 1 is the forecast for time period 2.Compute additional forecasts for time periods 4 through 9 using a 3-month moving
The U.S. Census Bureau publishes data on factory orders for all manufacturing, durable goods, and nondurable goods industries. Shown here are factory orders in the United States over a 13-year period ($ billion). a. Use these data to develop forecasts for the years 6 through 13 using a 5-year
The following data show the number of issues from initial public offerings (IPOs) for a 13-year period released by the Securities Data Company. Use these data to develop forecasts for the years 3 through 13 using exponential smoothing techniques with alpha values of .2 and .9.Let the forecast for
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