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Business Statistics Communicating With Numbers 2nd Edition Sanjiv Jaggia, Alison Kelly - Solutions

Consider a binary response variable y and an explanatory variable x that varies between 0 and 4. The linear model is estimated as Ŷ = −1.11 + 0.54x.a. Compute the estimated probability for x = 2 and x = 3.b. For what values of x is the estimated probability negative or greater than one?
Consider a binary response variable y and an explanatory variable x that varies between 0 and 50. The linear probability model is estimated as Ŷ = 0.92 − 0.02x.a. Compute the estimated probability for x = 25 and x = 40.b. For what values of x is the estimated probability negative?
Consider a binary response variable y and an explanatory variable x. The following table contains the parameter estimates of the linear probability model (LPM) and the logit model, with the associated p-values shown in parentheses.Variable................. LPM...................
Consider a binary response variable y and an explanatory variable x. The following table contains the parameter estimates of the linear probability model (LPM) and the logit model, with the associated p-values shown in parentheses.Variable................ LPM.............
Consider a binary response variable y and two explanatory variables x1 and x2. The following table contains the parameter estimates of the linear probability model (LPM) and the logit model, with the associated p-values shown in parentheses.Variable..................... LPM.............
Using 30 observations, the following regression output is obtained from estimating the linear probability model y = Î²0 + Î²1x + É›.a. What is the predicted probability when x = 20?b. Is x significant at the 5% level?
Using 30 observations, the following output was obtained when estimating the logit model.a. What is the predicted probability when x = 0.40?b. Is x significant at the 5% level?
Using 40 observations, the following output was obtained when estimating the logit model.a. What is the predicted probability when x1 = 15, x2 = 10, and x3 = âˆ’ 2?b. At the 5% significance level, which of the explanatory variables are significant?
Annabel, a retail analyst, has been following Under Armour, Inc., the pioneer in the compressiongear market. Compression garments are meant to keep moisture away from a wearer's body during athletic activities in warm and cool weather. Annabel believes that the Under Armour brand attracts a younger
Redo exercise 35 using a logit model.Exercise 35Annabel, a retail analyst, has been following Under Armour, Inc., the pioneer in the compressiongear market. Compression garments are meant to keep moisture away from a wearer's body during athletic activities in warm and cool weather. Annabel
According to the National Coalition on Health Care, there has been a steady decline in the proportion of Americans who have health insurance. The rising insurance premiums have made it difficult for small employers to offer insurance and those that do offer insurance are contributing a smaller
Redo exercise 37 using a logit model. Consider an individual with an income of $60,000. What is the probability that she has insurance coverage if her employer contributes 50% of the premium? What if her employer contributes 75% of the premium?Exercise 37According to the National Coalition on
According to a recent estimate, the divorce rate in England has fallen to a 26-year low (The Guardian, August 29, 2008). However, it is documented that the rate of divorce is more than twice as high for men and women aged 25 to 29. John Haddock is a sociologist from Sussex University who wants to
Redo exercise 39 using the logit model.Exercise 39According to a recent estimate, the divorce rate in England has fallen to a 26-year low (The Guardian, August 29, 2008). However, it is documented that the rate of divorce is more than twice as high for men and women aged 25 to 29. John Haddock is a
A researcher in the education department wants to determine if the number of hours that business students study per week at a state university varies by quarter. He conducts a survey where business students are asked how much they study per week in each of the three quarters. He defines a dummy
To encourage performance, loyalty, and continuing education, the human resources department at a large company wants to develop a regression-based compensation model for mid-level managers based on three variables: (1) business unitprofitability, (2) years with company, and (3) graduate degree in
Assembly line work can be tedious and repetitive. Therefore, it is not suited for everybody. Consequently, a production manager is developing a binary choice regression model to predict whether a newly hired worker will stay in the job for at least one year. Three explanatory variables will be
Seton Hall University is a Roman Catholic university situated in New Jersey, with easy access to New York City. Like most universities, it uses SAT scores and high school GPA as primary criteria for admission. The accompanying table shows a portion of data concerning information on admission (1 for
Redo exercise 50 using the logit model.Exercise 50Seton Hall University is a Roman Catholic university situated in New Jersey, with easy access to New York City. Like most universities, it uses SAT scores and high school GPA as primary criteria for admission. The accompanying table shows a portion
More and more parole boards are using risk assessment tools when trying to determine an individual's likelihood of returning to crime (The Boston Globe, February 20, 2011). Most of these models are based on a range of character traits and biographical facts about an individual. Many studies have
Redo exercise 52 using the logit model.Exercise 52More and more parole boards are using risk assessment tools when trying to determine an individual's likelihood of returning to crime (The Boston Globe, February 20, 2011). Most of these models are based on a range of character traits and
According to the World Health Organization, obesity has reached epidemic proportions globally. While obesity has generally been linked with chronic disease and disability, researchers argue that it may also affect salaries. In other words, the body mass index (BMI) of an employee is a predictor for
A recent study examined "sidewalk rage" in an attempt to find insight into anger's origins and offer suggestions for anger-management treatments (The Wall Street Journal, February 15, 2011). "Sidewalk ragers" tend to believe that pedestrians should behave in a certain way. For instance, slower
Jack Sprague is the relocation specialist for a real estate firm in the town of Arlington, Massachusetts. He has been working with a client who wishes to purchase a single-family home in Arlington. After seeing the information that Jack provided, the client is perplexed by the variability of home
The Chartered Financial Analyst (CFA®) designation is fast becoming a requirement for serious investment professionals. Although it requires successfully completing three levels of grueling exams, it also promises great careers with lucrative salaries. Susan Wayne works as a research analyst at
Consider the following sample data, consisting of 10 observations.a. Construct a 3-period moving average and plot it along with the actual series. Comment on smoothing.b. Use the 3-period moving average to make forecasts and compute the resulting MSE and MAD.c. Make a forecast for period 11.
Consider the following estimated trend models. Use them to make a forecast for t = 21.a. Linear Trend: Å¶ = 13.54 +1.08tb. Quadratic Trend: Å¶ = 18.28 + 0.92t - 0.01t2c. Exponential Trend :
Consider the following table, consisting of 20 observations of the variable y and time t.a. Plot the series along with the superimposed linear and exponential trends. Which trend model do you think describes the data well?b. Estimate a linear trend model and an exponential trend model for the
Consider the following table, consisting of 20 observations of the variable y and time t.a. Plot the series along with the superimposed linear and quadratic trends. Which trend model do you think describes the data well?b. Estimate a linear trend model and a quadratic trend model. Validate your
Despite the growth in digital entertainment, the nation's 400 amusement parks have managed to hold on to visitors, as the following data show:Year................. Visitors (in millions)2000..................................... 3172001.....................................
The potentially deadly 2009 Swine Flu outbreak was due to a new flu strain of subtype H1N1 not previously reported in pigs. When the World Health Organization declared a pandemic, the virus continued to spread in the United States, causing illness along with regular seasonal influenza viruses.
Rapid advances in technology have had a profound impact on the United States recording industry (The New York Times, July 28, 2008). While cassette tapes gave vinyl records strong competition, they were subsequently eclipsed by the introduction of the compact disc (CD) in the early 1980s. Lately,
Consider the following table, which lists a portion of the monthly unemployment rates (seasonally adjusted) in California from 2007-2010.Year.......... Month......... Unemployment Rate (%)2007.............. Jan.................................... 4.92007..............
Six years of quarterly data of a seasonally adjusted series are used to estimate a linear trend model as T̂t = 128.20 + 1.06t. In addition, quarterly seasonal indices are calculated asa. Interpret the first and fourth quarterly indices.b. Make a forecast for all four quarters of next year.
a. Interpret the third and fourth quarterly indices.b. Make a forecast for all four quarters of next year.
Ten years of monthly data of a seasonally adjusted series are used to estimate a linear trend model as T̂t = 24.50+ = 24.50 + 0.48t. In addition, seasonal indices for January and February are calculated as 1.04 and 0.92, respectively. Make a forecast for the first two months of next year.
Consider the following sample data, consisting of 20 observations.a. Construct a 5-period moving average and plot it along with the actual series. Comment on smoothing.b. Use the 5-period moving average to make forecasts and compute the resulting MSE and MAD.c. Make a forecast for period 21.
Consider the following 20 observations, representing quarterly information for 5 years.a. Calculate the 4-quarter centered moving average.b. Calculate the ratio-to-moving average.c. Calculate and interpret the seasonal indices for quarters 1 and 4.
Consider the following monthly observations for 5 years.a. Calculate the 12-month centered moving average.b. Calculate the ratio-to-moving average.c. Calculate and interpret the seasonal indices for April and November.
Consider the following 20 observations, representing quarterly information for 5 years.a. Plot the above series and discuss its trend and seasonal components.b. Use decomposition analysis to make forecasts with the exponential trend and seasonal indices. Compute the mean square errors of in-sample
Consider a portion of monthly sales data for 5 years for a growing firm.Year.............. Month............. Sales1 .......................Jan.............. 3451 .......................Feb............. 322⋮ ........................⋮...................... ⋮5.......................
Using the data from exercise 23, estimate (a) a linear trend model with seasonal dummies, and (b) an exponential trend model with seasonal dummies. Which of the two models has a lower MSE and MAD? Use the appropriate model to make forecasts for the next two months.Data From Exercise
Hybrid cars have gained popularity because of their fuel economy and the uncertainty regarding the price of gasoline. All automakers, including the Ford Motor Co., have planned to significantly expand their hybrid vehicle lineup (CNN.com, November 9, 2005). The following table contains quarterly
Consider a portion of monthly return data on 20-year Treasury Bonds from 2006-2010.Year................ Month................ Return (%)2006.................... Jan........................ 4.652006.................... Feb........................ 4.73⋮........................... ⋮
Using the data from exercise 26, estimate a linear trend model with seasonal dummy variables to make forecasts for the first three months of 2011.Data From 26Year................ Month................ Return (%)2006.................... Jan........................ 4.652006....................
The controller of a small construction company is attempting to forecast expenses for the next year. He collects quarterly data on expenses (in $1,000s) over the past 5 years, a portion of which is shown in the accompanying table.Year................. Quarter..............
Blockbuster Inc. has lately faced challenges by the growing online market (CNNMoney. com, March 3, 2009). Its revenue from rental stores has been sagging as customers are increasingly getting their movies through the mail or high-speed Internet connections. The following table contains a portion of
Consider the following sample data, consisting of 20 observations.a. Plot the above series and discuss the presence of random variations.b. Use the exponential smoothing method to make forecasts with Î± = 0.2. Compute the resulting MSE and MAD.c. Repeat the process with Î± = 0.4.d. Use the
Use the data from exercise 29 to:Year.......... Quarter.......... Revenue2001................. 1......... $1.4036832001................. 2........... 1.287625⋮............................. ⋮............................ ⋮2008................ 4........... 1.097712a. Estimate a linear trend
The following table lists a portion of the University of Michigan's Consumer Sentiment Index. This index is normalized to have a value of 100 in 1965 and is used to record changes in consumer morale.Year................... Month............... Consumer Sentiment2005....................... Jan
Using the data from exercise 31, fit an appropriate polynomial trend model along with seasonal dummies to make a forecast for November and December of 2010Exercise 31
Consider the following portion of data on the response variable y and the explanatory variable x.t................. y............... x1........... 27.96............ 29.882........... 30.15............ 21.07⋮...................... ⋮....................... ⋮12........... 24.47.......... 26.41a.
Consider the following portion of data on the variable y.t........................... y1...................... 29.322...................... 30.96⋮..................................... ⋮24.................... 48.58a. Estimate an autoregressive model of order 1, yt = β0 + β1yt−1 + εt, to
Consider the following portion of data on y and x.t........................y............... x1...................18.23.......... 17.302................... 19.82......... 16.05⋮......................... ⋮............... ⋮12................... 22.75.........13.66a. Estimate yt = β0 + β1xt−1
Consider the following portion of data on y and x.t...................... y.............................. x1.................. 56.96..................... 9,171.612.................. 57.28..................... 9,286.56⋮...................... ⋮...............................
Hiroshi Sato, an owner of a sushi restaurant in San Francisco, has been following an aggressive marketing campaign to thwart the effect of rising unemployment rates on business. He used monthly data on sales ($1,000s), advertising costs ($), and the unemployment rate (%) from January 2008 to May
The Phillips curve is regarded as a reliable tool for forecasting inflation. It captures the inverse relation between the rate of unemployment and the rate of inflation; the lower the unemployment in an economy, the higher is the inflation rate. Consider the following portion of monthly data on
A research analyst at an investment firm is attempting to forecast the daily stock price of Home Depot, using causal models. The following table shows a portion of the daily adjusted closing prices of Home Depot y and the Dow Jones Industrial Average x from August 14, 2009, to August 31,
Consider the following sample data, consisting of 20 observations.a. Use the 3-period moving average to make forecasts and compute the resulting MSE and MAD.b. Use the exponential smoothing method to make forecasts with Î± = 0.4. Compute the resulting MSE and MAD.c. Use the preferred method to
The U.S. housing market remains fragile despite historically low mortgage rates (AARP, July 2, 2010). Since the rate on 30-year mortgages is tied to the 10-year yield on Treasury bonds, it is important to be able to predict this yield accurately. The accompanying table shows a portion of the
The following table lists a portion of the percentage (share) of total shipment of music that falls in the category of country and rap/hiphop rock music from 1990-2008.Year..................... Country (in %)................ Rap/Hip-hop (in %)1990..................................
Tourism was hit hard by the international financial crisis that began in the fall of 2008. According to the Bureau of Economic Analysis (December 20, 2010), tourism spending has picked up, but it still remains below its peak, which occurred in 2007. The accompanying table shows a portion of
Consider the following portion of monthly data on price per gallon of unleaded regular gasoline in the U.S from January 2009 to December 2010.Year........................ Month................ Price Per Gallon2009............................ Jan
Consider the following portion of data on real estate loans granted by FDIC-insured Commercial Banks in the United States (in billions of U.S. dollars, base = 2007) from 1972 to 2007.Year................... Loans1972................. 489.271973................. 567.26⋮..........................
While U.S. inventory levels remain low, there is a slight indication of an increase in the U.S. business inventory-to-sales ratio, due to higher sales (The Wall Street Journal, December 15, 2010). The accompanying table shows a portion of seasonally adjusted inventory to- sales ratios from January
Revenue passenger-miles are calculated by multiplying the number of paying passengers by the distance flown in thousands. The accompanying table shows a portion of monthly data on revenue passenger-miles (in millions) from January 2006 through September 2010.Year......................
Use the data from exercise 46 to:Data From exercises 46Year...................... Month................... Revenue Passenger-Miles2006.......................... Jan....................................... 43.16522006.......................... Feb.......................................
The following data represent a portion of quarterly net sales (in millions of dollars) of Lowe's Companies, Inc., over the past five years.a. Estimate a linear trend model with seasonal dummy variables and compute the MSE and MAD.b. Estimate an exponential trend model with seasonal dummy variables
The S&P 500 Index is a valueweighted index of prices of 500 large-cap common stocks actively traded in the United States. A research analyst at an investment firm is attempting to forecast the daily stock price of Genzyme Corporation, one of the world's leading biotech companies, using both the
Rock 'n' roll is a form of music that evolved in the United States and quickly spread to the rest of the world. The interest in rock music, like any other genre, has gone through ups and downs over the years. The Recording Industry Association of America (RIAA) reports consumer trends on the basis
In August 2010, the Department of Commerce reported that economic weakness continues across the country, with consumer spending continuing to stagnate. The government is considering various tax benefits to stimulate consumer spending through increased disposable income. The consumption function is
Use the data for the share of total shipment of music that falls in the category of rock music from 1991-2008.a. Make a forecast for the share of rock music in 2009 using the exponential smoothing method with α = 0.4.b. Make a forecast for the share of rock music in 2009 using the exponential
According to the Census Bureau, the number of people below the poverty level has been steadily increasing (CNN, September 16, 2010). This means many families are finding themselves there for the first time. The following table shows a portion of the percent of families in the United States who are
Consider the following table, which shows a portion of the closing prices of the S&P 500 Index for 21 trading days in November 2010.Date.................... S&P Price1-Nov..................... 1184.382-Nov.....................
The accompanying table shows a portion of monthly data on seasonally adjusted inflation and unemployment rates in the United States from January 2009 to November 2010.a. Use a 3-period moving average and exponential smoothing with Î± = 0.6 to make in-sample forecasts for unemployment. Use the
Fried dough is a popular North American food associated with outdoor food stands at carnivals, amusement parks, fairs, and festivals, etc. Usually dusted with powdered sugar and drenched in oil, it is not particularly good for you but it sure is tasty! Jose Sanchez owns a small stall at Boston
Madelyn Davis is a research analyst for a large investment firm. She has been assigned the task of forecasting sales for Walmart Stores, Inc., for fiscal year 2011. She collects quarterly sales for Walmart Stores, Inc. (in millions $) for the 10- year period 2001 through 2010, a portion of which is
Gary Martin is a research analyst at an investment firm in Chicago. He follows the oil industry and has developed a pretty sophisticated model that forecasts an oil company's stock price. However, given the recent strife in the Middle East, he wonders if simpler causal models might do a better job
Consider the following price data from 1994 to 2002.a. Compute the simple price index using 1994 as the base year.b. Determine the percentage change in prices from 1994 to 1998.
Consider the following simple price index created with a base year of 2004.a. Update the index numbers using a revised base year of 2008.b. Determine the percentage change in price from 2004 to 2012.c. Determine the percentage change in price from 2008 to 2012.
Consider the following price and quantity data for three products from 2008 to 2010.a. Compute the simple price index for each product, using 2008 as the base year.b. Compare the relative price movements of the three products?
Use the price and quantity information in Exercise 12 to compute the following aggregate price indices, given a base year of 2008:a. The unweighted aggregate price indexb. The Laspeyres price indexc. The Paasche price index?
Consider the following average monthly prices for regular gasoline in California in 2008.a. Construct a simple price index with January 2008 as the base.b. Determine the percentage change in the average gasoline price in California from January to June.
The following table shows the monthly adjusted closing price per share of Microsoft Corporation for 2009.a. Construct a simple price index with January 2009 as the base.b. What is the percentage price change in July relative to January?c. What is the percentage price change in December relative to
The MIT Sloan School of Management is one of the leading business schools in the U.S. The following table contains the tuition data for the masters program in the Sloan School of Management.a. Use 2004 as the base year to form a simple price index for tuition.b. Use 2007 as the base year to form a
According to dollar cost averaging, a fixed amount of money is invested periodically in a portfolio. Consequently, more units of a financial asset are purchased when prices are low and fewer units are purchased when prices are high. Robert Dudek follows dollar cost averaging by making a monthly
JJ Diner is a small mom and pop restaurant in Lincoln, Nebraska. They offer three choices for breakfast: omelets, pancakes, or cereal. The average prices (in dollars) for these options for 2007, 2008, and 2009 are shown in the accompanying table.a. Compute and interpret the simple price index for
The following table shows the number (in 1,000s) of breakfasts sold at JJ DinerUse this information, along with the price data provided in Exercise 18, toa. Compute and interpret the Laspeyres price index.b. Compute and interpret the Paasche price index?
You bought a corporate bond last year for $980. You received a coupon payment (interest) of $60 and the bond is currently selling for $990. What is the(a) Income yield,(b) Capital gains yield,(c) Total return on the investment?
With the collapse of house prices that started in 2006, the American Dream has become a nightmare for many of the 75 million Americans who own a home (CBS Evening News, February 2, 2010). However, the drop in house prices has not been uniform across the country. The accompanying table represents
Consider the following table, which reports the sale (quantity in 1,000s) of homes by region for 2007, 2008, and 2009.Use this information, along with the price data provided in Exercise 20, toa. Compute and interpret the Laspeyres aggregate home price index for the U.S.b. Compute and interpret the
The nominal values for four years are given by 32, 37, 39, and 42. Convert these values to real terms if the price index values for the corresponding years are given by 100, 102, 103, 108?
An item increases in value from 240 to 280 in one year. What is the percentage change in the value of this item? Compute the percentage change in real terms if overall prices have increased by 5% for the same period?
Let revenues increase by 10% from $100,000 to $110,000. Calculate the percentage change in real terms if the relevant price index increases by 4% from 100 to 104?
The following table represents the nominal values of an item and the corresponding price index for 2007 and 2008.Year............... Nominal Value.............. Price Index2007............................... 38...................... 1122008............................... 40......................
The following table represents the nominal values of an item and the corresponding price index from 2009 to 2011.a. Compare the percentage change in the nominal values with the corresponding real values from 2009 to 2010.b. Compare the percentage change in the nominal values with the corresponding
Economists often look at retail sales data to gauge the state of the economy. This is especially so in a recession year, when consumer spending has decreased. Consider the following table, which shows U.S. monthly nominal retail sales for 2009. Sales are measured in millions of dollars and have
Japan was the first Asian country to challenge the dominance of the U.S. in the 1980s. However, since then, its economy has been in a slow but relentless decline (The New York Times, October 16, 2010). This country has been trapped in low growth and a downward spiral of prices, known as deflation.
Each month the Current Employment Statistics (CES) program surveys numerous businesses and government agencies in order to obtain detailed data on earnings of workers. Consider the following data on the national average of hourly earnings for 2008. Also included is the corresponding consumer price
The price of a stock has gone up from $24 to $35 in one year. It also paid a year-end dividend of $1.20. What is the stock's (a) Income yield,(b) Capital gains yield,(c) Total return?

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