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Essentials Of Business Statistics Communicating With Numbers 1st Edition Sanjiv Jaggia, Alison Kelly - Solutions
Using data from 50 workers, a researcher estimates Wage = β0 + β1Education + β2Experience + β3Age + , where Wage is the hourly wage rate and Education, Experience, and Age are the years of higher education, the years of experience, and the age of the worker, respectively. A
Osteoporosis is a degenerative disease that primarily affects women over the age of 60. A research analyst wants to forecast sales of StrongBones, a prescription drug for treating this debilitating disease. She uses the model Sales β0 + β1Population + β2Income + , where Sales refers to the
A sociologist believes that the crime rate in an area is significantly influenced by the area’s poverty rate and median income. Specifically, she hypothesizes crime will increase with poverty and decrease with income. She collects data on the crime rate (crimes per 100,000 residents), the
A realtor in Arlington, Massachusetts, is analyzing the relationship between the sale price of a home (Price), its square footage (Sqft), the number of bedrooms (Beds), and the number of bathrooms (Baths). She collects data on 36 recent sales in Arlington in the first quarter of 2009 for the
Education reform is one of the most hotly debated subjects on both state and national policy makers’ list of socioeconomic topics. Consider a linear regression model that relates school expenditures and family background to student performance in Massachusetts using 224 school districts. The
American football is the highest paying sport on a per-game basis. The quarterback, considered the most important player on the team, is appropriately compensated. A sports statistician wants to use 2009 data to estimate a multiple linear regression model that links the quarterback’s salary with
The accompanying table shows a portion of data consisting of the selling price, the age, and the mileage for 20 used sedans. The entire data set, labeled Car_Prices, can be found on the text website.a. Determine the sample regression equation that enables us to predict the price of a sedan on the
The accompanying table shows a portion of data consisting of the rent, the number of bedrooms, the number of bathrooms, and the square footage for 40 apartments in the college town of Ann Arbor, Michigan. The entire data set, labeled AnnArbor_Rental, can be found on the text website.a. Determine
In a simple linear regression based on 25 observations, the following intermediate data are given: Σ(yi - )2 = 1250 and Σ(yi - )2 = 1500.a. Calculate se2 and se.b. Calculate R2.
In a simple linear regression based on 30 observations, it is found that SSE = 2540 and SST = 13,870.a. Calculate se2 and se.b. Calculate R2.
In a multiple regression with two explanatory variables, the following intermediate data are given: n = 50, Σ(yi - )2 = 35 , and Σ(yi - )2 = 90.a. Calculate the standard error of the estimate.b. Calculate the coefficient of determination R2.
In a multiple regression with four explanatory variables and 100 observations, it is found that SSR = 4.75 and SST = 7.62.a. Calculate the standard error of the estimate.b. Calculate the coefficient of determination R2.c. Calculate adjusted R2.
The following ANOVA table was obtained when estimating a simple linear regression model.a. Calculate the standard error of the estimate.b. Calculate the coefficient of determination. Interpret thisvalue.
The following ANOVA table was obtained when estimating a simple linear regression model.a. Calculate se.b. Calculate and lnterpretR2.
The following ANOVA table was obtained when estimating a multiple linear regression model.a. Calculate the standard error of the estimate.b. Calculate and interpret the coefficient of determination.c. Calculate the adjustedR2.
The following ANOVA table was obtained when estimating a multiple regression model.a. Calculate the standard error of the estimate.b. Calculate and interpret the coefficient of determination.c. Calculate the adjustedR2.
When estimating the selling price of a used sedan as a function of its age using the model Price = β0 + β1Age + , a researcher gets the following ANOVA results:a. How many observations did the researcher use?b. What is the standard error of the estimate?c. Calculate and
When estimating the sales of a firm as a function of its advertising expenditures using the model Sales = β0 + β1Advertising + , an analyst obtains the following ANOVA results:a. What proportion of the variability in sales is explained by advertising expenditures?b. What
The director of college admissions at a local university is trying to determine whether a student’s high school GPA or SAT score is a better predictor of the student’s subsequent college GPA. She formulates two models:Model 1. College GPA = β0 + β1High School GPA + Model 2. College GPA = β0
For a sample of 41 New England cities, a sociologist studies the crime rate in each city (crimes per 100,000 residents) as a function of its poverty rate (in %) and its median income (in $1,000s). A portion of the regression results is shown in the following table.a. Calculate the standard error of
A financial analyst uses the following model to estimate a firm’s stock return: Return = β0 + β1P/E + β2P/S + , where P/E is a firm’s price-to-earnings ratio and P/S is a firm’s price-to-sales ratio. A portion of the regression results is shown in the following
Access the data Test_Scores from the text website.a. Estimate a student’s final grade as a function of his/her midterm grade.b. Find the standard error of the estimate.c. Find and interpret the coefficient of determination.
Access the data Property_Taxes from the text website.a. Estimate a home’s property taxes as a linear function of the size of the home (measured by its square footage).b. What proportion of the variability in property taxes is explained by the home’s size?c. What proportion of the variability in
Is it defense or offense that wins football games? Consider the following data, which include a team’s winning record (Win), the average number of yards gained, and the average number of yards allowed during the 2009 NFL season. The complete data, labeled Football, can be found on the text
Executive compensation has risen dramatically beyond the rising levels of an average worker’s wage over the years. This has been a hot topic for discussion, especially with the crisis in the financial sector and the controversy over the federal bailout. The government is even considering a
In a simple linear regression based on 30 observations, it is found that b1 = 3.25 and se(bj) = 1.36. Consider the hypotheses: H0: β1 = 0 and HA: β1 ≠ 0.a. Calculate the value of the test statistic.b. Approximate the p-value.c. At the 5% significance level, what is the conclusion? Is the
In a simple linear regression based on 25 observations, it is found that b1 = 0.5 and se(bj) = 0.3. Consider the hypotheses: H0: β1 ≤ 0 and HA: β1 > 0.a. At the 5% significance level, find the critical value(s).b. Calculate the value of the test statistic.c. What is the conclusion to the
In a simple linear regression based on 30 observations, it is found that b1 = 7.2 and se(bj) = 1.8. Consider the hypotheses: H0: β1 ≥ 10 and HA: β1 < 10.a. At the 5% significance level, find the critical value(s).b. Calculate the value of the test statistic.c. What is the conclusion to the
Consider the following regression results based on 20 observations.a. Specify the hypotheses to determine if the intercept differs from zero. Perform this test at the 5% significance level.b. Construct the 95% confidence interval for the slope coefficient. At the 5% significance level, does the
Consider the following regression results based on 40 observations.a. Specify the hypotheses to determine if the slope differs from minus one.b. At the 5% significance level, find the critical value(s).c. Calculate the value of the test statistic.d. Does the slope differ from minus one?Explain.
When estimating a multiple linear regression model based on 30 observations, the following results were obtained.a. Specify the hypotheses to determine whether x1 is linearly related to y. At the 5% significance level, use the p-value approach to complete the test. Are x1 and y linearly related?b.
The following ANOVA table was obtained when estimating a multiple linear regression model.a. How many explanatory variables were specified in the model? How many observations were used?b. Specify the hypotheses to determine whether the explanatory variables are jointly significant.c. Compute the
In order to examine the relationship between the selling price of a used car and its age, an analyst uses data from 20 recent transactions and estimates Price = β0 + β1Age + . A portion of the regression results is shown in the accompanying table.a. Specify the competing hypotheses in order
A marketing manager analyzes the relationship between the annual sales of a firm (in $100,000s) and its advertising expenditures (in $10,000s). He collects data from 20 firms and estimates Sales =β0 + β1Advertising + . A portion of the regression results is shown in the accompanying table.a.
A recent study on the evolution of mankind shows that, with a few exceptions, world-record holders in the 100-meter dash have progressively gotten bigger over time (The Wall Street Journal, July 22, 2009). The following table shows runners who have held the record, along with their record-holding
An economist examines the relationship between changes in short-term interest rates and long-term interest rates. He believes that changes in short-term rates are significant in explaining long-term interest rates. He estimates the model Dlong = β0 + β1Dshort + , where Dlong is the change in
For a sample of 20 New England cities, a sociologist studies the crime rate in each city (crimes per 100,000 residents) as a function of its poverty rate (in %) and its median income (in $1,000s). A portion of the regression results is shown in the accompanying table.a. Specify the sample
A researcher estimates the following model relating the return on a firm’s stock as a function of its price-to-earnings ratio and its price-to-sales ratio: Return = β0 + β1P/E +β2P/S + . A portion of the regression results is shown in the accompanying table.a. Specify the sample regression
Akiko Hamaguchi is a manager at a small sushi restaurant in Phoenix, Arizona. Akiko is concerned that the weak economic environment has hampered foot traffic in her area, thus causing a dramatic decline in sales. In order to offset the decline in sales, she has pursued a strong advertising
Access the data labeled Test_Scores from the text website. Use the information on 32 students to estimate a student’s final grade as a linear function of a student’s midterm grade. At the 1% significance level, is a student’s midterm grade significant in explaining a student’s final grade?
Access the data labeled Property_Taxes from the text website. The data represent the size of a home (in square feet) and its property taxes owed by the owner (in $) in an al fluent suburb 30 miles outside New York City. Use the data to estimate a home’s property taxes as a linear function of its
Caterpillar, Inc. manufactures and sells heavy construction equipment worldwide. The performance of Caterpillar’s stock is likely to be strongly influenced by the economy. For instance, during the subprime mortgage crisis, the value of Caterpillar’s stock plunged dramatically.Monthly
A Realtor examines the factors that influence the price of a house in Arlington, Massachusetts. He collects data on recent house sales (Price) and notes each house’s square footage (Sqft) as well as its number of bedrooms (Beds) and number of bathrooms (Baths). A portion of
On the first day of class, an economics professor administers a test to gauge the math preparedness of her students. She believes that the performance on this math test and the number of hours studied per week on the course are the primary factors that predict a student’s score on the final
In an attempt to determine whether or not a linear relationship exists between the price of a home (in $1,000s) and the number of days it takes to sell the home, a real estate agent collected data from recent sales in his city and estimated the following model: Price = β0 + β1Days + . A
A sociologist wishes to study the relationship between an individual’s age and his/her happiness. He interviews 24 individuals and collects data on his/her age and happiness score, measured on a scale from 0 to 100. A portion of the data is shown; the entire data set, labeled Happiness_Age,
In response to the global financial crisis, Federal Reserve leaders continue to keep the short-run target interest rate near zero. While the Fed controls short-term interest rates, long-term interest rates essentially depend on supply/demand dynamics, as well as longer-term interest rate
The homeownership rate in the United States was 67.4% in 2009. In order to determine if homeownership is linked with income, 2009 state level data on the homeownership rate (Ownership) and median household income (Income) were collected. A portion of the data is shown below; the entire data set,
The accompanying table gives a portion of data on gold prices, the Consumer Price Index (CPI), and the New York Stock Exchange (NYSE) Index for the United States for the period 1980–2010. The entire data set, labeled Gold_NYSE, can be found on the text website.An investment is supposed to be
A research analyst is trying to determine whether a firm’s price-earnings (P/E) and price-sales (P/S) ratios can explain the firm’s stock performance over the past year. AP/E ratio is calculated as a firm’s share price compared to the income or profit earned by the firm per
There has been a lot of discussion regarding the relationship between Scholastic Aptitude Test (SAT) scores and test-takers’ family income (New York Times, August 27,2009). It is generally believed that the wealthier a student’s family, the higher the SAT score. Another commonly used predictor
Many of today’s leading companies, including Google, Microsoft, and Facebook, are based on technologies developed within universities. Lisa Fisher is a business school professor who would like to analyze university factors that enhance innovation. She collects data on 143 universities
A researcher interviews 50 employees of a large manufacturer and collects data on each worker’s hourly wage (Wage), years of higher education (EDUC), experience (EXPER), and age (AGE). The entire data set, labeled Hourly_Wage, can be found on the text website.a. Estimate: Wage = β0 + β1EDUC +
Access the data AnnArbor_Rental from the text website. The data represent the rent, the number of bedrooms, the number of bathrooms, and the square footage for 40 apartments in the college town of Ann Arbor, Michigan.a. Determine the sample regression equation that enables us to predict the rent on
Akiko Hamaguchi, the manager at a small sushi restaurant in Phoenix, Arizona, is concerned that the weak economic environment has hampered foot traffic in her area, thus causing a dramatic decline in sales. Her cousin in San Francisco, Hiroshi Sato, owns a similar restaurant, but he has seemed to
Megan Hanson, a Realtor in Brownsburg, Indiana, would like to use estimates from a multiple linear regression model to help prospective sellers determine a reasonable asking price for their homes. She believes that the following four factors influence the asking price (Price) of a house: (1) the
Apple Inc. has established a unique reputation in the consumer electronics industry with its development of products such as the iPod, the iPhone, and the iPad. As of May 2010,Apple had surpassed Microsoft as the most valuable company in the world (New York Times, May 26, 2010). Michael Gomez is a
Consider a linear regression model where y represents the response variable, x is a quantitative explanatory variable, and d is a dummy variable. The model is estimated as = 14.8 + 4.4x - 3.8d.a. Interpret the dummy variable coefficient.b. Compute for x = 3 and d = 1.c. Compute for x = 3 and
Using 50 observations, the following regression output is obtained from estimating y = β0 + β1x + β2d1 + β3d2 + .a. Compute y̅ for x = 250, d1 = 1 and d2 = 0; then compute y̅ for x = 250, d1 = 0 and d2 = 1.b. Interpret d1 and d2. Are both dummy variables individually
House price y is estimated as a function of the square footage of a house x and a dummy variable d that equals 1 if the house has ocean views. The estimated house price, measured in $1,000s, is given by y̅ = 118.90 + 0.12x + 52.60d.a. Compute the predicted price of a house with ocean views and
A sociologist is studying the relationship between consumption expenditures y of families in the United States, family income x, and whether or not the family lives in an urban or rural community. She collects data on 50 families, a portion of which is shown in the accompanying table. The entire
One of the theories regarding initial public offering (IPO) pricing is that the initial return y (change from offer to open price) on an IPO depends on the price revision x (change from pre-offer to offer price). Another factor that may influence the initial return is whether or not it is a high
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
In an attempt to “time the market,†a financial analyst studies the quarterly returns of a stock. He uses the model y = β0 + β1d1 + β2d2 + β3d3 + where y is the quarterly return of a stock, d1 is a dummy variable that equals 1 if quarter 1 and 0 otherwise, d2 is a dummy
In the United States, baseball has always been a favorite pastime and is rife with statistics and theories. While baseball purists may disagree, to an applied statistician no topic in baseball is too small or hypothesis too unlikely. In a recent paper, researchers at Wayne State University showed
A manager at an ice cream store is trying to determine how many customers to expect on any given day. Overall business has been relatively steady over the past several years, but the customer count seems to have ups and downs. He collects data over 30 days and records the number of customers, the
A researcher wonders whether males get paid more, on average, than females at a large firm. She interviews 50 employees and collects data on each employee’s hourly wage (Wage), years of higher education (EDUC), experience (EXPER), age (AGE), and gender. The GENDER dummy variable equals 1 if
A government researcher is analyzing the relationship between retail sales and the gross national product (GNP). He also wonders whether there are significant differences in retail sales related to the quarters of the year. He collects 10 years of quarterly data. A portion is shown in the
The issues regarding executive compensation have received extensive media attention. The government is even considering a cap on high-lying salaries for executives (New York Times, February 9, 2009). Consider a regression model that links executive compensation with the total assets of the firm and
In a simple linear regression based on 30 observations, the following information is provided: = -6.92 + 1.35x and se = 2.78. Also, se (0) evaluated at x = 30 is 1.02.a. Construct the 95% confidence interval for E(y) if x = 30.b. Construct the 95% prediction interval for y if x equals 30.c.
In a multiple regression with 40 observations, the following sample regression equation is obtained: y̅ = 12.8 + 2.6x1 - 1.2x2 with se = 5.84. Also, when x1 equals 15 and x2 equals 6, Se (y̅0) = 2.20.a. Construct the 95% confidence interval for E(y) if x1 equals 15 and x2 equals 6.b. Construct
Consider the following sample data:a. Find the sample regression line, = b0 + b1x.b. Construct the 95% confidence interval for E(y) if x = 15.c. Construct the 95% prediction interval for y if x =15.
Consider the following sample data:a. Find the sample regression equation, = b0 + b1x1 + b2x2.b. Construct the 95% confidence interval for E(y) if x1 equals 50 and x2 equals 20.c. Construct the 95% prediction interval for y if x1 equals 50 and x2 equals 20.
Using the data in the accompanying table estimate the model: Salary = β0 + β1Education + ε, where Salary is measured in $1,000s and Education refers to years of higher education.a. Construct the 90% confidence interval for the expected salary for an individual who completed 6 years of
With the data in the accompanying table, estimate GPA = β0 + β1GRE + , where GRE is a student’s score on the math portion of the Graduate Record Examination and GPA is the student’s grade point average in graduate school.a. Construct the 90% confidence interval for the expected GPA for
Access the data labeled Debt_Payments from the text website and estimate Debt = β0 + β1Income + ε, where Debt is the average debt payments for a household in a particular city (in $) and Income is the city’s median income (in $1,000s).a. Construct the 95% confidence interval for expected debt
Access the data labeled Arlington_Homes from the text website and estimate: Price = β0 + β1Sqft + β2Beds + β3Baths + ε, where Price, Sqft, Beds, and Baths refer to home price, square footage, number of bedrooms, and number of bathrooms, respectively. Construct the 95% confidence interval for
Access the data, labeled BMI_Salary, from the text website to estimate a regression model using the salary of a college-educated worker as the response variable and BMI and Race as the two explanatory variables. Race is a dummy variable that equals 1 if white and 0 if non-white.a. Construct and
Access the data, labeled Urban_Rural, from the text website to estimate a regression model using consumption as the response variable. The explanatory variables include income and a dummy variable that equals 1 for urban, 0 otherwise.a. Construct and interpret the 99% confidence interval for the
Access the data, labeled Professor_Salary, from the text website. These data were used in the introductory case of this chapter. Recall that we estimated our preferred model as y̅ = 39.43 + 1.24x + 13.89d, where y represents salary (in $1,000s), x represents experience (in years), and d is a
Access the data, labeled Retafl_Sales, from the text website. Estimate the model y = β0 + β1x + β2d1 + β3d2 + β4d3 + ε, where y is Retail Sales, x is GNP, d1 is a dummy variable that equals 1 for quarter 1, d2 is a dummy variable that equals 1 for quarter 2, and d3 is a dummy variable that
Using 20 observations, the multiple regression model y = β0 + β1x1 + β2x2 + ε was estimated. Excel produced the following relevant results.a. At the 5% significance level, are the explanatory variables jointly significant?b. At the 5% significance level, is each explanatory variable
A simple linear regression, y = β0 + β1x + ε, is estimated with cross-sectional data. The resulting residuals e along with the values of the explanatory variable x is shown in the accompanying table.a. Graph the residuals e against the values of the explanatory variable x and look for any
A simple linear regression, y = β0 + β1x + ε is estimated with time series data. The resulting residuals e and the time variable t are shown in the accompanying table.a. Graph the residuals against time and look for any discernible pattern.b. Which assumption is being violated? Discuss its
Numerous studies have shown that watching too much television hurts school grades. Others have argued that television is not necessarily a bad thing for children (Mail Online, July 18, 2009). Like books and stories, television not only entertains, it also exposes a child to new information about
Access the data labeled Work_Experfence from the text website. The data contain information on salary (in $) and work experience (in years) of 100 employees in a marketing firm. Estimate a model y = β0 + β1x + ε where y is salary and x is work experience.a. Explain why you would be concerned
Consider the monthly rent (Rent) of a home in Ann Arbor, Michigan, as a function of the number of bedrooms (Beds), the number of bathrooms (Baths), and square footage (Sqft).a. Access the data labeled AnnArbor_Rental from the text website and estimate Rent = β0 + β1Beds + β2Baths + β3Sqft +
Healthy living has always been an important goal for any society. In a recent ad campaign for Walt Disney, First Lady Michelle Obama shows parents and children that eating well and exercising can also be fun (USA TODAY, September 30, 2010). Consider a regression model that conjectures that fruits
In August 2010, the Department of Commerce reported that economic weakness persists 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
A financial analyst would like to determine whether the return on Fidelity€™s Magellan mutual fund varies depending on the quarter; that is, if there is a seasonal component describing return. He collects 10 years of quarterly return data. A portion is shown in the accompanying table; the
In a seminal study, researchers documented race-based hiring in the Boston and Chicago labor markets (American Economic Review, September 2004). They sent out identical resumes to employers, half with traditionally African-American names and the other half with traditionally Caucasian names.
According to the U.S. Department of Health and Human Services, African-American women have the highest rates of being overweight compared to other groups in the United States. Individuals are considered overweight if their body mass index (BMI) is 25 or greater.Consider the following data on
According to the Centers for Disease Control and Prevention, life expectancy at age 65 in America is about 18.7 years. Medical researchers have argued that while excessive drinking is detrimental to health, drinking a little alcohol every day, especially wine, may be associated with an increase in
The homeownership rate in the United States was 67.4% in 2009. In order to determine if homeownership is linked with income, 2009 state level data on the homeownership rate (Ownership) and median household income (Income) were collected. A portion of the data is shown below; the entire data set,
A researcher studies the relationship between SAT scores, the test-taker’s family income (Income), and his/her grade point average (GPA). Data are collected from 24 students. A portion of the data is shown; the entire data set, labeled SAT, can be found on the text website.Estimate: SAT =
The manager of a diner wants to reevaluate his staffing needs depending on variations in customer traffic during the day. He collects data on the number of customers served along with four dummy variables representing the morning, afternoon, evening, and night shifts. The dummy variable Morning
Consider a regression model for per capita income y. The explanatory variables consist of the percentage of the population in the United States that is (a) without a high school diploma x1, (b) foreign born x2, and (c) non-English speaking x3. The accompanying table shows a portion of the data; the
George believes that returns of mutual funds are influenced by annual turnover rates and annual expense ratios. In order to substantiate his claim, he randomly selects eight mutual funds and collects data on each fund’s five-year annual return (Return), its annual holding turnover rate
A government researcher examines the factors that influence a city’s crime rate. For 41 cities, she collects the crime rate (crimes per 100,000 residents), the poverty rate (in %), the median income (in $1,000s), the percent of residents younger than 18, and the percent of residents older
A research analyst is trying to determine whether a firm’s price-earnings (P/E) and price-sales (P/S) ratios can explain the firm’s stock performance over the past year. Generally, a high P/E ratio suggests that investors are expecting higher earnings growth in the future compared to
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