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Business Statistics for Contemporary Decision Making 6th Edition Ken Black - Solutions
A corporation owns several companies. The strategic planner for the corporation believes dollars spent on advertising can to some extent be a predictor of total sales dollars. As an aid in long-term planning, she gathers the following sales and advertising information from several of the companies
Investment analysts generally believe the interest rate on bonds is inversely related to the prime interest rate for loans; that is, bonds perform well when lending rates are down and perform poorly when interest rates are up. Can the bond rate be predicted by the prime interest rate? Use the
Is it possible to predict the annual number of business bankruptcies by the number of firm births (business starts) in the United States? The following data published by the U.S. Small Business Administration, Office of Advocacy, are pairs of the number of business bankruptcies (1000s) and the
It appears that over the past 45 years, the number of farms in the United States declined while the average size of farms increased. The following data provided by the U.S. Department of Agriculture show five-year interval data for U.S. farms. Use these data to develop the equation of a regression
Can the annual new orders for manufacturing in the United States be predicted by the raw steel production in the United States? Shown on the next page are the annual new orders for 10 years according to the U.S. Census Bureau and the raw steel production for the same 10 years as published by the
Determine the equation of the regression line for the following data, and compute theresiduals.
Solve for the predicted values of y and the residuals for the data in Problem 12.6. The data are provided hereagain:
Solve for the predicted values of y and the residuals for the data in Problem 12.7. The data are provided hereagain:
Solve for the predicted values of y and the residuals for the data in Problem 12.8. The data are provided hereagain:
Solve for the predicted values of y and the residuals for the data in Problem 12.9. The data are provided hereagain:
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. Using this regression model and the data given in problem 12.10 (and provided here again), solve for the predicted values of y and the
The equation of a regression line isy = 50.506 – 1.646xAnd the data are as follows.Solve for the residuals and graph a residual plot. Do these data seem to violate any of the assumptions ofregression?
Wisconsin is an important milk-producing state. Some people might argue that because of transportation costs, the cost of milk increases with the distance of markets from Wisconsin. Suppose the milk prices in eight cities are as follows.Cost of Milk Distance from Madison(per gallon) (miles)$2.64
Graph the following residuals, and indicate which of the assumptions underlying regression appear to be in jeopardy on the basis of the graph.xy – ẏ213 .......... -11216 .......... -5227 .......... -2229 .......... -1237 .......... +6247 ..........+10263 ..........+12
Graph the following residuals, and indicate which of the assumptions underlyingregression appear to be in jeopardy on the basis of the graph.xy – ẏ10 .......... +611 .......... +312 .......... -113 ..........-1114 .......... -315 .......... +216 .......... +517 .......... +8
Study the following Minitab Residuals Versus Fits graphic for a simple regression analysis. Comment on the residual evidence of lack of compliance with the regressionassumptions.
Determine the sum of squares of error (SSE) and the standard error of the estimate (se) for Problem 12.6. Determine how many of the residuals computed in Problem 12.14 (for Problem 12.6) are within one standard error of the estimate. If the error terms are normally distributed, approximately how
Determine the SSE and the se for Problem 12.7. Use the residuals computed in Problem 12.15 (for Problem 12.7) and determine how many of them are within ±1se and ±2se. How do these numbers compare with what the empirical rule says should occur if the error terms are normally distributed?
Determine the SSE and the se for Problem 12.8. Think about the variables being analyzed by regression in this problem and comment on the value of se.In Problem 12.8Advertising Sales12.5 ..............1483.7 .............. 5521.6 ..............33860.0 ..............99437.6 ..............5416.1
Determine the SSE and se for Problem 12.9. Examine the variables being analyzed by regression in this problem and comment on the value of se.In Problem 12.9Bond Rate Prime Interest Rate5% ..............16%12 ..............69 ..............815 ..............47 ..............7
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 standard error of the estimate and comment on it.In problem 12.10Business Bankruptcies Firm
Use the data from problem 12.19 and determine the se.In problem 12.19y = 50.506 – 1.646xAnd the data are asfollows.
Determine the SSE and the se for Problem 12.20. Comment on the size of se for this regression model, which is used to predict the cost of milk.In Problem 12.20Cost of Milk Distance from Madison(per gallon) (miles)$2.64 .........1,2452.31 ......... 4252.45 .........1,3462.52 ......... 9732.19
Determine the equation of the regression line to predict annual sales of a company from the yearly stock market volume of shares sold in a recent year. Compute the standard error of the estimate for this model. Does volume of shares sold appear to be a good predictor of a company’s sales?
Compute r2 for Problem 12.24 (Problem 12.6). Discuss the value of r2 obtained.(in Problem12.6)
Compute r2 for Problem 12.25 (Problem 12.7). Discuss the value of r2 obtained.In (Problem12.7)
Compute r2 for Problem 12.26 (Problem 12.8). Discuss the value of r2 obtained.(In Problem 12.8).Advertising Sales12.5 ..............1483.7 .............. 5521.6 ..............33860.0 ..............99437.6 ..............5416.1 .............. 8916.8 ..............12641.2 ..............379
Compute r2 for Problem 12.27 (Problem 12.9). Discuss the value of r2 obtained.(in Problem 12.9).Bond Rate Prime Interest Rate5% ..............16%12 ..............69 ..............815 ..............47 ..............7
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.In problem 12.10Business Bankruptcies Firm Births(1000)
The Conference Board produces a Consumer Confidence Index (CCI) that reflectspeople’s feelings about general business conditions, employment opportunities, and their own income prospects. Some researchers may feel that consumer confidence is a function of the median household income. Shown here
Test the slope of the regression line determined in Problem 12.6. Use α = .05.in Problem12.6.
Test the slope of the regression line determined in Problem 12.7. Use α = .01.In Problem12.
Test the slope of the regression line determined in Problem 12.8. Use α = .10.in Problem 12.8Advertising Sales12.5 ..............1483.7 .............. 5521.6 ..............33860.0 ..............99437.6 ..............5416.1 .............. 8916.8 ..............12641.2 ..............379
Test the slope of the regression line determined in Problem 12.9. Use a 5% level of significance.In Problem 12.9Bond Rate Prime Interest Rate5% ..............16%12 ..............69 ..............815 ..............47 ..............7
Test the slope of the regression line developed in Problem 12.10. Use a 5% level of significance.in Problem 12.10Business Bankruptcies Firm Births(1000) (10,000)34.3 ..............58.135.0 ..............55.438.5 ..............57.040.1 ..............58.535.5 ..............57.437.9 ..............58.0
Study the following analysis of variance table, which was generated from a simple regression analysis. Discuss the F test of the overall model. Determine the value of t and test the slope of the regressionline.
Construct a 95% confidence interval for the average value of y for Problem 12.6. Use x = 25.In Problem12.6
Construct a 90% prediction interval for a single value of y for Problem 12.7; use x = 100. Construct a 90% prediction interval for a single value of y for Problem 14.2; use x = 130. Compare the results.Which prediction interval is greater? Why?In Problem12.7
Construct a 98% confidence interval for the average value of y for Problem 12.8; use x = 20. Construct a 98% prediction interval for a single value of y for Problem 14.3; use x = 20.Which is wider? Why?In Problem 12.8Advertising Sales12.5 ..............1483.7 .............. 5521.6
Construct a 99% confidence interval for the average bond rate in Problem 12.9 for a prime interest rate of 10%. Discuss the meaning of this confidence interval.in Problem 12.9Bond Rate Prime Interest Rate5% ..............16%12 ..............69 ..............815 ..............47 ..............7
Determine the equation of the trend line for the data shown below on U.S. exports of fertilizers to Indonesia over a five-year period provided by the U.S Census Bureau. Using the trend line equation, forecast the value for the year 2011.Year Fertilizer ($ millions)2005 ........11.92006
Shown below are rental and leasing revenue figures for office machinery and equipment in the United States over a seven-year period according to the U.S. Census Bureau. Use these data to construct a trend line and forecast the rental and leasing revenue for the year 2010 using these data.Year
After a somewhat uncertain start, e-commerce sales in the United States have been growing for the past several years. Shown below are quarterly e-commerce sales figures ($ billions) released by the Census Bureau for the United States over a three-year period. Use these data to determine the
Determine the Pearson product-moment correlation coefficient for the followingdata.
Use the following data for parts (a) through (f).a. Determine the equation of the least squares regression line to predict y by x.b. Using the x values, solve for the predicted values of y and the residuals.c. Solve for se.d. Solve for r2.e. Test the slope of the regression line. Use α = .01.f.
Use the following data for parts (a) through (g).a. Determine the equation of the simple regression line to predict y from x.b. Using the x values, solve for the predicted values of y and the residuals.c. Solve for SSE.d. Calculate the standard error of the estimate.e. Determine the coefficient of
If you were to develop a regression line to predict y by x, what value would the coefficient of determinationhave?
Determine the equation of the least squares regressionline 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
Executives of a video rental chain want to predict the success of a potential new store. The company's researcher begins by gathering information on number of rentals and average family income from several of the chain's present outlets.Rentals Average Family Income ($1,000)710 .............65529
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, some units may serve more
Shown here are the total employment labor force figures for the country of Romania over a 13-year period published in LABORSTA. Develop the equation of a trend line through these data and use the equation to predict the total employment labor force of Romania for the year 2011.Year Total Employment
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 Treasure Yield1.57% ...........3.05%2.23
According to the National Marine Fisheries Service, the current landings in millions of pounds of fish by U.S. fleets are almost double what they were in the 1970s. In other words, fishing has not faded as an industry. However, the growth of this industry has varied by region as shown in 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 sales of the company? Show are sales income and advertising cost data for seven companies published by Advertising Age.Use the data to develop a regression line to predict the amount of advertising by sales. Compute se
Can the consumption of water in a city be predicted by 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 ............. 103◦56 .............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 negative?d.
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
Study the following Minitab residual diagnostic graphs. Comment on any possible violations of regressionassumptions.
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 43 countries (1800 coffee houses) outside of
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 x =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 x =13.
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
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 their significance.The regression equationis
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 t tests.
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 t tests.In Problem13.6
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
Study the Minitab output shown in Problem 13.7. Comment on the overall strength of the regression model in light of S, R2, and adjusted R2.In Problem 13.7The regression equationis
Study the Minitab output shown in Problem 13.8. Comment on the overall strength of the regression model in light of S, R2, and adjusted R2.
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.
Using the regression output obtained by working Problem 13.11, comment on the overall strength of the regression model using S, R2, and adjusted R2.
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.
Study the Excel output shown in Problem 13.13. Comment on the overall strength of the regression model in light of S, R2, and adjusted R2.
Study the Minitab residual diagnostic output that follows. Discuss any potential problems with meeting the regression assumptions for this regression analysis based on the residualgraphics.
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 modelfit.
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 regression 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.
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 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 formy = b0bx1 ϵusing the following data to predict y from x. From a scatter plot and Tukey’s 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 x1and x2 in the model in addition to x21 and x22, and the interaction term x1 x2. Comment on the overall strength of the model and the significance of each predictor. Develop a regression model with the same
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