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business
statistics for business and economics

Questions and Answers of Statistics For Business And Economics

Consider the following time series data.a. Construct a time series plot. What type of pattern exists in the data?b. Show the four-quarter and centered moving average values for this time series.c.
Refer to exercise 35.a. Deseasonalize the time series using the adjusted seasonal indexes computed in part (c) of exercise 35.b. Using Minitab or Excel, compute the linear trend regression equation
The following table reports prices and usage quantities for two items in 2009 and 2011.a. Compute price relatives for each item in 2011 using 2009 as the base period.b. Compute an unweighted
A large manufacturer purchases an identical component from three independent suppliers that differ in unit price and quantity supplied. The relevant data for 2009 and 2011 are given here.a. Compute
R&B Beverages, Inc., provides a complete line of beer, wine, and soft drink products for distribution through retail outlets in central Iowa. Unit price data for 2008 and 2011 and quantities sold
Data on quantities of three items sold in 1997 and 2011 are given here along with the sales prices of the items in 1997. Compute a weighted aggregate quantity index for 2011. Quantity Sold Item 1997
A trucking firm handles four commodities for a particular distributor. Total shipments for the commodities in 1996 and 2011, as well as the 1996 prices, are reported in the following table.Develop a
An automobile dealer reports the 1994 and 2011 sales for three models in the following table. Compute quantity relatives and use them to develop a weighted aggregate quantity index for 2011 using the
Use the price data in exercise 18 to compute a Paasche index for the shipping cost if 2011 quantities are 4000, 3000, 7500, and 3000 for each of the four products.Data From Exercise 18:Nickerson
Boran Stockbrokers, Inc., selects four stocks for the purpose of developing its own index of stock market behavior. Prices per share for a 2009 base period, January 2011, and March 2011 follow.
Compute the price relatives for the four stocks making up the Boran index in exercise 20. Use the weighted aggregates of price relatives to compute the January 2011 and March 2011 Boran indexes.Data
A major manufacturing company reports the quantity and product value information for 2007 and 2011 in the table that follows. Compute a weighted aggregate quantity index for the data. Comment on what
The commercial division of a real estate firm is conducting a regression analysis of the relationship between x, annual gross rents (in thousands of dollars), and y, selling price (in thousands of
The Transactional Records Access Clearinghouse at Syracuse University reported data showing the odds of an Internal Revenue Service audit. The following table shows the average adjusted gross income
Refer to the data in exercise 31. Consider a model in which only Industry is used to predict Delay. At a .01 level of significance, test for any positive autocorrelation in the data.Data From
The pursuit of a higher education degree in business is now international. A survey shows that more and more Asians choose the master of business administration (MBA) degree route to corporate
The Energy Information Administration of the U.S. Department of Energy provided time series data for the U.S. average price per gallon of conventional regular gasoline between January 2007 and March
Suppose you also calculated the standard errors for the coefficients for experience, education, and sex as 2,000, 85, and 2,500, respectively. How would your answer to part (b) of question 24
Estimate the regression of Chrysler’s return on assets against its debt/equity ratio. Compute the Durbin–Watson statistic. Does autocorrelation exist?Use MINITAB and the Above information to
Redo question 42 using the data for Ford.Question 42Estimate the regression of Chrysler’s return on assets against its debt/equity ratio. Compute the Durbin–Watson statistic. Does autocorrelation
Redo question 42 using the data for GM.Question 42Estimate the regression of Chrysler’s return on assets against its debt/equity ratio. Compute the Durbin–Watson statistic. Does autocorrelation
Assume that the investor’s initial wealth is $40,000 and that her utility function is U = W1/2. What is the expected utility of the portfolio described in question 61?Question 61Assume that the
Use the information given in question 48 to find the probability that it will take more than 5 days to find the 11th error. Find the probability that it will take between 3 and 10 days to find the
Use the information given in question 50 to find the proportion of viewers who will be able to recall the commercial after 7 days.Question 50An advertising executive believes that the length of time
Use the information given in question 54 to find the probability that the life of the car battery will be greater than 5 years. Find the probability that the life of the battery will be between 4 and
A random sample of 75 observations reveals that the sample mean is 20. You know that the population standard deviation is 5. Construct a 90 % confidence interval for the population mean.
Use the information given in question 27 to test H0: μ = 1,100 versus H1: μ ≠ 1,100 at the .10 level of significance.Question 27 You are given the information x = 1,050, Sx = 250, and n = 20.
In a taste test using 400 randomly selected people, 220 preferred a new brand of coffee to the leading brand. Test, at the 1 % significance level, the alternative hypothesis that at least 52 % prefer
In question 78, a statistician argues that the length of delay may depend on the airport from which the airplane departs. Accordingly, the data were regrouped to reflect departure sites X, Y, and Z.
If, in question 68, 90% of the bottles contain more than 16 oz of milk, what is the probability that fewer than 3 of the 30 bottles that the agency bought contain more than 16 oz of milk?Question
In question 70, what is the probability that of the 100 cars test-driven, more than 35 cars get more than 45 miles per gallon? How many of the 100 cars tested would you expect to get more than 45
Compare simple regression to multiple regression. When would you use simple regression? When would you use multiple regression?
In simple regression, the geometric interpretation is to fit a line that best describes the relationship between x and y. What is the geometric interpretation of multiple regression when there are
Discuss the differences between the assumptions of the simple and the multiple linear regression models.
We can test the significance of a simple regression either by using a t-test to test the slope coefficient or by using an F-test to test the significance of the model.How does our approach differ
Explain how the number of degrees of freedom available for estimating σ2 of the error term is related to the number of variables in the regression.
Briefly compare the concepts of simple correlation, partial correlation, and multiple correlation.
Compare the ways the regression coefficients are interpreted in simple regression and in multiple regression.
What is a partial regression coefficient? How do we measure it?
What is multicollinearity? Why is it a problem in multiple regression?
Suppose an NFL scout is interested in what physical attributes make for a good quarterback. He collects data on the height and weight of 8 quarterbacks and their performance ratings for the year. The
Using the information given in question 10, compute SSR, SSE, SST, and R2.Also use an F-test to test the significance of the model.
Using the results from question 10, forecast the performance rating for a quarterback who is 6 ft 1 in. tall and weighs 200 lb. Construct a 95 %confidence interval around this forecast.Question
The chairperson of the finance department at Rutgers University would like to find the relationship between undergraduate grade point average (UGPA) and GMAT scores on graduate grade point average
Suppose we were interested in testing the joint significance of b1 and b2 in terms of data from question 13. That is, the null hypothesis is H0: β1 = β2 = 0.(a) Explain how we would conduct such a
Use the data and results from question 13 to construct 90 % confidence intervals for b1 and b2.Question 13The chairperson of the finance department at Rutgers University would like to find the
Suppose a student has a 3.85 undergraduate GPA and a GMAT score of 575.(a) Forecast this student’s graduate GPA.(b) Construct a 90 % confidence interval for this forecast. Use Eqs. 15.30 and
Suppose a labor economist is interested in the effect of experience and education on income. He obtains the following regression.Interpret the regression coefficients for EXPER and EDUC. INCOME = 24,
Suppose you calculate sb1 = 325 and sb2 = 285 , and you know that 50 observations were used to estimate the model. Test the significance of the regression coefficients in question 17.Question
An agent for Decade 100 Real Estate Company is interested in developing a model that explains the value of a piece of real estate. She collects data on the following variables:(a) Which variables
Suppose you estimate a regression using 20 observations and 16 independent variables. You compute R2 to be .98. Explain why R2 may not be an appropriate measure of the goodness of fit. Can you think
Suppose a travel consultant is interested in the relationship between people’s incomes and the amount of money they spend for vacations. He chooses to estimate the regressionDo you think he will
Thomas Chen, an education professor, is interested in the relationship among final exam scores, midterm exam scores, and hours studied for the final. He collects the following data.(a) Estimate the
Using the data and your results from question 22, test the individual significance of b1 and b2. Also construct a 99 % confidence interval for b1 and b2.Question 22Thomas Chen, an education
Using the data and your results from question 22, forecast the final exam score for a student who scored 97 on the midterm and studied 6 1/2 h for the final.Construct a 90 % confidence interval for
In multiple regression, we can test the significance of the individual regression coefficients by using a t-test, or we can test the joint significance of the coefficients by using an F-test. Is it
An economist at the National Academy of Movie Theater Owners wants to estimate the demand for movie tickets. He chooses to estimate the equation. where QT, = a + B, PT, + B (GNP) + & QT, quantity of
Suppose the economist of question 26 collects the following data.(a) Estimate the demand for movie tickets.(b) Do the coefficients carry the correct signs?(c) If you were going to use a t-test to
Use your results from question 27 to compute R2 and R-2. Also use an F-test to test the joint significance of the regression.Question 27Suppose the economist of question 26 collects the following
Construct 95 % confidence intervals for the coefficients b1 and b2 from the regression in question 27.Question 27Suppose the economist of question 26 collects the following data.(a) Estimate the
Suppose you have obtained the following 1992 and 1993 forecasts of GNP and ticket prices.(a) Forecast the quantity of tickets sold for 1992 and 1993.(b) Construct 90 % confidence intervals for these
Suppose the economist in question 26 is interested in estimating the price and income elasticity of demand for movie tickets. He can do this by taking the natural logarithms of QT, PT, and GNP and
Use a t-test to test the significance of the estimated elasticities.
Use an F-test to test the joint significance of the price and income elasticity.
Use MINITAB to answer question.An investment analyst is interested in developing an equation to forecast the earnings per share of a company. He collects the following data for five companies.(a)
Use MINITAB to answer question.Construct 90 % confidence intervals for α, β1, and β2, using the results from question 35.Question 35Suppose the analyst of question 34 decides on the following
Use MINITAB to answer question.Forecast the EPS for a company with $400 in sales and a cost of $65. Construct a 99 % confidence interval for this forecast. Use Eqs. 15.30 and 15.33.Eqs. 15.30Eqs.
You estimate a regression using a computer package that generates the following output.(a) Compute the t-values for the coefficients.(b) Say the sample used to estimate the regression consisted of 27
Use the foregoing information to construct 95 % confidence intervals for the parameters.
Buford Lightfoot, a stock market analyst, is interested in finding a model to describe the returns for different stocks. He estimates the following regression: Rit = a + BRm,t + Bli,t + &t where Rm1
Construct a 90 % confidence interval for the parameter estimates from question 40. Assume n = 30.Question 40Buford Lightfoot, a stock market analyst, is interested in finding a model to describe the
Say you know that the return on the S&P 500 will be 3 % next month and that the industry index next month will be 2. Forecast stock i’s return.
Suppose you fit the modelusing 35 data points and obtain SSE = .56 and R2 = .85. Test the null hypothesis that all bs are equal to zero against the alternative hypothesis that at least one of the bs
Again consider question 43. Examine SSE and R2, and explain whether the model provides a good fit.Question 43Suppose you fit the modelusing 35 data points and obtain SSE = .56 and R2 = .85. Test the
Suppose you estimate the modelCompute R2. Does the model provide a good fit? z = a +Bx + Bx2 + & using 25 observations and obtain (2 - 2) = 2.45 and (z-z) = 3.65
Explain why, given the same independent variables, the confidence interval for the mean value of y is always narrower than the corresponding confidence interval for any other value of y.
You are given the following information:(a) Compute the least-squares estimate for intercept and slopes (b) Compute the t-values for slopes b1 and b2 Cov (y,x) = 65, Var (x) = 4.5 Var (x) = 4.2 Cov
Use the data from question 47 to compute(a) R2(b) Adjusted R2(c) F statisticsQuestion 47You are given the following information:(a) Compute the least-squares estimate for intercept and slopes (b)
Use the data of question 47 and the answers of questions 47 and 48 to predict y if x1 = 7.5 and x2 = 6.5. In addition, please also calculate 95% confidence interval and 95 % prediction
The admissions officer at Poindexter U. would like to determine the effect of high school GPA and SAT scores on undergraduate GPA. He collects the following data on six students.(a) Calculate the
Suppose we are interested in testing the joint significance of b1 and b2. That is, the null hypothesis is H0: β1 - β2 = 0. Test the joint significance of β1 and β1.
Use the data and results from question 50 to construct 90 % confidence intervals for β1 and β2.Question 50The admissions officer at Poindexter U. would like to determine the effect of high school
Suppose a student with a 3.85 high school GPA and an SAT score of 555 applies for admission to Poindexter U.(a) Forecast this student’s undergraduate GPA.(b) Construct a 90 % confidence interval
You have been hired as an economist for the Federal Reserve Bank of New York. Your job is to forecast future interest rates. Summarize the theory of the interest rate, and formulate a mathematical
You have been hired as a consultant for AT&T. Formulate a mathematical model that could be used to estimate the demand for telephone service.
You have been hired as an economist for the Public Utility Commission of Wisconsin. The agency needs an estimate of the demand for electricity in order to determine what rates the electric companies
Researchers interested in determining the relationship between a firm’s annual sales and its expenditures on research and development (x1), television advertising(x2), and all other advertising
A statistician is interested in using product price and the amount of advertising to predict the sales of a product. Several combinations of price and advertising are tried, with the following
Use the following equation to answer parts (a) through (d). = -1.67 +2.46x - 5.48x2
An economist states that wages should be inversely related to the rate of unemployment and should be positively related to prices. Test these claims at the .10 Type I error level, using the following
How are simple and multiple regression similar? How are they different?
The closing prices of six stocks on the last day of last month seem to be quite highly correlated with their latest reported earnings per share figures and with the percentage of earnings growth they
A regression equation was found to be for this equation was .95. The values of x1 ranged from -10 to 15 and those of x2 from -20 to -50. Which of the following statements are true?(a) Variable x2
A regression equation was found to be Which of the following statements are true?(a) A 1-unit increase in x1 causes y to increase by 14 units.(b) Variable y is more highly correlated with x1 than
A regression analysis has two independent variables (x1 and x2).(a) What does it mean if x1 and x2 are independent of each other? In that case, what is the correlation between them?(b) Is saying that
Use the return information for 3-month T-bills, the NYSE Index, Chrysler, Ford, and GM for the 3-year period from January 1985 through December 1987 on Chap. 18. Suppose of interest now is to
Use the return information for 3-month T-bills, the NYSE Index, Chrysler, Ford, and GM for the 3-year period from January 1985 through December 1987 on Chap. 18. Suppose of interest now is to
Use the return information for 3-month T-bills, the NYSE Index, Chrysler, Ford, and GM for the 3-year period from January 1985 through December 1987 on Chap. 18. Suppose of interest now is to
Use the return information for 3-month T-bills, the NYSE Index, Chrysler, Ford, and GM for the 3-year period from January 1985 through December 1987 on Chap. 18. Suppose of interest now is to
For the return data with NYSE Index being explained by Ford and Chrysler, suppose we expect the returns for Ford and Chrysler are 0.0229 and 0.0337, respectively. Forecast the return for NYSE and

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