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business
business statistics a first course
Questions and Answers of
Business Statistics A First Course
According to the Investment Company Institute, the number of U.S. mutual shareholder accounts (millions)were as shown in the table for years 1990 (coded as t 1) through 2007. Construct a
For the shipment data listed in Exercise 18.45, construct a first-order autoregressive forecasting equation and make a forecast for period 19.
Analysis of a time series consisting of weekly visits(in thousands) to a corporate website has led to the following autoregressive forecasting equation: ˆyt 5 34.50 10.58yt21 2 0.72yt22. If there
A regression model has 2 independent variables and 16 observations, and the calculated Durbin-Watson d statistic is 2.78. What, if any, conclusion will be reached in testing for autocorrelation of
A regression model has 3 independent variables and 20 observations, and the calculated Durbin-Watson d statistic is 0.91. What, if any, conclusion will be reached in testing for autocorrelation of
The least-squares regression equation ˆy 5 15.2 110.7t has been fitted to the shipment data in the table.Calculate the Durbin-Watson d statistic and test for positive autocorrelation of the
The least-squares regression equation yˆ 5 98.1 1 5.0t has been fitted to the shipment data given here. Calculate the Durbin-Watson d statistic and test for positive autocorrelation of the residuals
What is the Durbin-Watson test for autocorrelation, and how can it be useful in evaluating the relevance of a given regression model that has been fitted to a set of time series data?
When autocorrelation of the residuals is present, what effect can this have on interval estimation and significance tests regarding the regression model involved?
Using the MAD criterion, determine which one of the equations developed in Exercise 18.8 is the better fit to the data in that exercise. Repeat the evaluation, using the MSE criterion.
Using the MAD criterion, determine which one of the equations developed in Exercise 18.7 is the better fit to the data in that exercise. Repeat the evaluation, using the MSE criterion.
The following data are the number of Harley-Davidson motorcycles sold worldwide for 2003 through 2006 (thousands). Given these data and the trend equations, use the MAD criterion to determine which
The following data are the wellhead prices for domestically produced natural gas, in dollars per thousand cubic feet, from 2001 through 2008. Given these data and the trend equations shown here, use
How do the MAD and MSE criteria differ in their approach to evaluating the fit of an estimation equation to a time series?
The quarterly seasonal indexes for a firm’s electricity consumption are 115, 92, 81, and 112 for quarters I–IV. It has been forecast that electricity consumption will be 850,000 kilowatt-hours
A firm predicts it will use 560,000 gallons of water next year. If the seasonal index of water consumption is 135 for the second quarter of the year, what is the forecast for water consumption during
If a time series is such that sales are consistently increasing from one year to the next, will exponential smoothing tend to produce forecasts that are (a) over or (b) under the sales that are
For the data of Exercise 18.9, use the weighting constant 0.6 and exponential smoothing to determine the forecast for 2008.
For the data of Exercise 18.7, use the weighting constant 0.5 and exponential smoothing to determine the forecast for 2008.
The U.S. trade deficit with Canada (billions of dollars) from 2000 through 2007 is reported as shown in the table. Using exponential smoothing and the smoothing constant 0.7, what deficit would
When exponential smoothing is used in fitting a curve to a time series, the approach is slightly different from its application to forecasting. Compare the appropriate formulas and point out how they
Based on annual truck rentals over the years, a rental firm has developed the quadratic trend equation yˆ 450 20x 7.2x2, with x 1 for 2005. Forecast y for 2013; for 2015.
An appliance repair shop owner has fitted the quadratic trend equation yˆ 90 0.9x 3x2 to a time series of annual repair orders, with y the number of repair orders and x 1 for 2005.
The linear trend equation ˆ y 120 4.8x has been developed, where yˆ estimated sales (thousands of dollars) and x 1 for the year 1999. What level of sales would be forecast for 2013; for
A mail-order firm has found the following seasonal indexes for the number of calls received each month. Below the seasonal indexes is the actual number of calls (thousands) per month during 2009.a.
Given the data of Exercise 18.13, (a) determine the monthly seasonal indexes for January through December, then(b) use these indexes to deseasonalize the original time series.
Given the degree-day data of Exercise 18.11,(a) determine the monthly seasonal indexes for January through December, then (b) use these indexes to deseasonalize the original time series.
A major amusement park has the following number of visitors each quarter from 2005 through 2009:a. Construct the four-quarter centered moving average for these data and determine the percentages of
The state of Texas has reported the following quarterly gross sales for the in-state accommodation and food services industry for the years 2004–2008.a. Construct the four-quarter centered moving
The seasonal indexes for a convention center’s bookings are 83, 120, 112, and 85 for quarters 1– 4, respectively. What percentage of the center’s annual bookings tend to occur during the second
In determining seasonal indexes for the months of the year, a statistician finds the total of the “unadjusted”seasonal indexes is 1180 instead of 12 ? 100, or 1200.What correction must be made to
For the data of Exercise 18.15:a. Fit an exponentially smoothed curve with smoothing constant 5 0.6.b. For these data, describe the appearance of the exponentially smoothed curve when the smoothing
For the data of Exercise 18.15, determine the centered moving average for N 5 2; for N 5 4.
For the data of Exercise 18.13, fit an exponentially smoothed curve with smoothing constant 5 0.4; with smoothing constant 5 0.7. Which constant provides more “smoothing” and why? Which curve is
For the data of Exercise 18.11, fit an exponentially smoothed curve with smoothing constant 5 0.4; with smoothing constant 5 0.7. Which constant provides more“smoothing” and why? Which curve is
The following data describe U.S. manufacturers’shipments of general aviation jet aircraft from 1989 through 2008.a. Construct a graph of the time series. Does the overall trend appear to be upward
For the data of Exercise 18.13:a. Obtain the centered moving average for N 5 4; for N 5 12.b. When N 5 12 months, the centered moving average is relatively smooth compared to N 5 4. Aside from the
The following data describe the monthly volume for an urban courier service. Data are in thousands of pieces handled.a. Construct a graph of the time series. Does the overall trend appear to be
For the data of Exercise 18.11:a. Obtain the centered moving average for N 5 4; for N 5 12.b. When N 5 12 months, the centered moving average is relatively smooth compared to when N 5 4. Aside from
According to the U.S. Energy Information Administration, a heating degree-day is a relative measurement of outdoor temperature that indicates how far the average daily temperature is below 65°
For the data in Exercise 18.9, determine the centered moving average for N 5 2; for N 5 4.
The following data show residential and commercial natural gas consumption (quadrillion Btu)from 1992 through 2007.a. Construct a graph of the time series, then superimpose a three-year centered
From 2000 through 2007, the value of U.S. exports to Mexico was as shown below. Data are in billions of dollars.a. Fit a linear trend equation to the time series. Using this equation, determine the
U.S. cellular phone subscribership has been reported as shown here for the 1996–2007 period.a. Fit a linear trend equation to the time series. Using this equation, determine the trend estimate for
Fit a linear trend equation to these data showing the value of shipments of food products in billions of dollars.What is the trend estimate for 2015? Year: 2004 2005 2006 2007 Shipments: $512.3
Fit a linear trend equation to the following data describing average hourly earnings of U.S. production workers. What is the trend estimate for 2013? Year: 2004 2005 2006 2007 Average Hourly
The trend equation ˆ y 5 1200 1 35x has been fitted to a time series for industry worker days lost due to job-related injuries. If x 5 1 for 1995, estimate the number of worker days lost during 2012.
The estimated trend value of community water consumption is 400,000 gallons for a given month.Assuming that the cyclical component is 120% of normal, with the seasonal and irregular components 70%
For each of the following, indicate which time series component is represented. Explain your reasoning.a. The proprietor of a movie theater finds Saturday is the most popular day of the week for
What are the four components of a time series, and to what kind of variation in the series does each refer?
Based on your analysis in Case Question 2, and even considering the results from a complete regression that uses all of the possible predictive variables identified in Case Question 1, does there
Provide further assistance to Sam Easton by carrying out and interpreting the results of an appropriate stepwise regression designed to indicate which of the predictive variables mentioned in Case
As a first step in helping Sam Easton better understand how the sales price of a residential property is determined, construct a correlation matrix for the variables PRICE, SQFEET, BEDROOMS, AGE,
Based on your analysis in Case Question 2, and even considering the results from a complete regression that uses all of the possible predictive variables, does there seem to be very much variation in
Because the committee is very interested in using predicted first-year MBA grade point average in measuring the quality of applicants to its program, assist the members further by carrying out and
The committee wishes to use first-year MBA grade point average as its measure of the quality of a student.As a first step in assisting committee members, construct a correlation matrix and briefly
Repeat step 2, but this time perform a stepwise regression analysis. Minitab and Excel users should refer to the following notes. Identify the variables that were introduced and interpret the
Using y 5 stock price (variable 8) as the dependent variable, carry out a conventional multiple regression analysis using variables 2–7, 9, and 11–16. Excel users, see note 1, which follows.
Generate a correlations matrix that includes variables 2–9 and 11–16. (Variable 10 would be meaningless here because its values are 1–7 for the 7 company categories.)Do the correlations “make
As indicated in the chapter-opening vignette, the National Football League quarterback passer rating is somewhat of a mystery to most observers. Data file XR17073 includes the passer rating for 32
Repeat parts (b)–(d) of Exercise 17.71, with Test 1 as the dependent variable, and Test 2, Test 3, Test 4, and Final Exam as the independent variables.
The students in a training program have taken four tests along with a final exam, with the scores shown in the table. The data are also in file XR17071.a. Construct the correlation matrix for these
Given the situation and variables described in Exercise 17.66 and data file XR17066, use y 5 percent of sales quota in performing a stepwise regression using the other variables as predictors.
Data file XR17069 lists a variety of information for a selection of aircraft. The variables and their units are: operating cost (dollars per hour), number of seats, speed (mph), flight range (miles),
The Dow Jones Global Indexes describe over 3000 companies worldwide that represent more than 80% of the equity capital in the world’s stock markets. Data file XR17068 shows the quarterly indexes
For the loan delinquency data in Exercise 17.64 and listed in file XR17064, fit a multiplicative model and use it to estimate the delinquency rate for all insured commercial bank loans when the
The sales director for an industrial supplies firm has collected information describing the performance and personal characteristics of 80 members of her sales force. The data in file XR17066 include
The production engineer for the manufacturing plant in Exercise 17.61 has just included another variable:the worker’s gender, coded as 1 5 female and 0 5 male. File XR17065 contains the expanded
For loans at insured commercial banks, the Federal Financial Institutions Examination Council has reported the percentage of various kinds of loans that were at least 30 days in delinquency during
The data in file XR17063 include the wind chill index (how cold it “feels”) at different combinations of outside temperature (degrees Fahrenheit) and wind speed(miles per hour). For y 5 wind
For loans at insured commercial banks, the Federal Financial Institutions Examination Council has reported the percentage of various kinds of loans that were at least 30 days in delinquency during
The data in file XR17063 include the wind chill index (how cold it “feels”) at different combinations of outside temperature (degrees Fahrenheit) and wind speed(miles per hour). For y 5 wind
The data in the table show the number of years it took for selected technological innovations to spread to 25% of the U.S. population. The data are also in file XR17062. For y 5 years to spread and x
Each workstation in the final assembly area of a large manufacturing facility has a “backlog” area to hold units that are to be processed. A production engineer believes there could be a
For 1995 through the first half of 2009, PricewaterhouseCoopers and the National Venture Capital Association reported quarterly venture capital investments (trillions of dollars) and the number of
J.K. Rowling’s popular Harry Potter books have tended to become thicker with each new edition. The publication year and page count for U.S. editions for the first seven books were as shown on the
As reported by the Recording Industry Association of America, the percentage of recorded music dollar sales in CD format was as shown here for the years 2000 through 2007. The data are also in file
Using the data file for Exercise 17.55:a. Apply stepwise regression with the rating by board member 9 as the dependent variable and the ratings by the other 8 members as the set of independent
Using the data file for Exercise 17.55:a. Apply stepwise regression with the rating by board member 1 as the dependent variable and the ratings by the other 8 members as the set of independent
An officer training program has 9 board members who provide ratings for the candidates. The high and low scores are dropped before the overall rating is computed.For a sample of 28 persons from the
For the situation and data described in Exercise 17.17, perform conventional multiple regression and stepwise regression analyses on the data, then compare the results of the two approaches. Use
For the situation, data, and variables described in Exercise 17.15, perform conventional multiple regression and stepwise regression analyses on the data, then compare the results of the two
For the situation, data, and variables described in Exercise 17.16, perform conventional multiple regression and stepwise regression analyses on the data, then compare the results of the two
For the data in Exercise 17.45, and using total nonrenewable energy production as the dependent variable, perform conventional multiple regression and stepwise regression analyses on the data, then
For the data in Exercise 17.44, and using Sunday circulation as the dependent variable, perform conventional multiple regression and stepwise regression analyses on the data, then compare the results
The following Minitab printout is for a stepwise regression with 10 independent variables and 50 observations:a. List the order in which the independent variables have been introduced.b. What is the
The two largest values in a correlation matrix are the 0.850 correlation between y and x4, and the 0.790 correlation between y and x9. During a stepwise regression analysis, x4 is the first
In general, on what basis are independent variables selected for entry into the equation during stepwise regression?
What is stepwise regression, and when is it desirable to make use of this multiple regression technique?
For the years 1998–2008, production in the U.S. energy sector included the quantities shown here.The variables represent total energy production as well as energy production from nonrenewable
Circulation (millions) for Sunday newspapers versus morning and evening daily papers for 1999–2007 are shown here. The data are also in file XR17044. With Sunday circulation as the dependent
For the situation and variables in Exercise 17.17, use data file XR17017 and generate a correlation matrix for these independent variables: number of aircraft, number of employees, and number of
For the situation and variables in Exercise 17.16, use data file XR17016 and generate a correlation matrix for the independent variables. Examine the correlation matrix and comment on the possible
Four predictor variables are being considered for use in a linear regression model. Given the accompanying correlation matrix, does it appear that multicollinearity could be a problem? E F G H 1 x1
A linear regression analysis was performed using x1 as a predictor variable. The p-value associated with the regression coefficient for x1 was 0.02, and the sign of the coefficient was negative.
In linear regression models, for what types of uses or applications would multicollinearity tend to be a problem?Are there any applications or uses for which multicollinearity would not be a problem?
One of the indicators that multicollinearity is present is when a variable that is known to be an important predictor ends up having a partial regression coefficient that is not significant. What are
What is a correlation matrix, and what role does it play in multiple regression?
For the situation and variables in Exercise 17.16, fit a multiplicative model and use it to estimate the rental revenue for a company with 80,000 cars in service and 2500 rental locations. The
For the situation and variables in Exercise 17.17, fit a multiplicative model and use it to estimate the total operating revenue for an airline with 2000 employees and 10,000 departures. The
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