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statistics

Questions and Answers of Statistics

Using data from 50 workers, a researcher estimates WageÂ = Î²0 + Î²1Education + Î²2Experience + Î²3Age + , where Wage is the hourly wage rate and Education, Experience, and Age are the
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
A sociologist believes that the crime rate in an area is significantly influenced by the areaâ€™s poverty rate and median income. Specifically, she hypothesizes crime will increase with poverty
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
Education reform is one of the most hotly debated subjects on both state and national policy makersâ€™ list of socioeconomic topics. Consider a linear regression model that relates school
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
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
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,
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.
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
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
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
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.
When estimating the selling price of a used sedan as a function of its age using the model Price = Î²0 + Î²1Age + , a researcher gets the following ANOVA results:a. How many
When estimating the sales of a firm as a function of its advertising expenditures using the model Sales = Î²0 + Î²1Advertising + , an analyst obtains the following ANOVA
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
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
A financial analyst uses the following model to estimate a firmâ€™s stock return: Return = Î²0 + Î²1P/E + Î²2P/S + , where P/E is a firmâ€™s price-to-earnings ratio and P/S is a
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
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
Is it defense or offense that wins football games? Consider the following data, which include a teamâ€™s winning record (Win), the average number of yards gained, and the average number of yards
Executive compensation has risen dramatically beyond the rising levels of an average workerâ€™s wage over the years. This has been a hot topic for discussion, especially with the crisis in the
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
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
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
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.
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
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%
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
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 = Î²0 + Î²1Age + . A portion of the
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
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,
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
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
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
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
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%
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
Caterpillar, Inc. manufactures and sells heavy construction equipment worldwide. The performance of Caterpillarâ€™s stock is likely to be strongly influenced by the economy. For instance, during
A Realtor examines the factors that influence the priceÂ of a house in Arlington, Massachusetts. He collects data on recent house sales (Price) and notes each houseâ€™s square footage
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
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
A sociologist wishes to study the relationship between an individualâ€™s age and his/her happiness. He interviews 24 individuals and collects data on his/her age and happiness score, measured on
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
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
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 1980â€“2010. The
A research analyst is trying to determine whether a firmâ€™s price-earnings (P/E) and price-sales (P/S) ratios can explain the firmâ€™s stock performance over the past year. AP/E ratio is
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
Many of todayâ€™s leading companies, including Google,Â Microsoft, and Facebook, are based on technologies developed within universities. Lisa Fisher is a business school professor who
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
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
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
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.
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
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.
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
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
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.
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
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
In an attempt to â€œtime the market,â€ a financial analyst studies the quarterly returns of a stock. He uses the model y = Î²0 + Î²1d1 + Î²2d2 + Î²3d3 + where y is the quarterly
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
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
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 employeeâ€™s hourly wage (Wage), years of higher
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 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).
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%
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) =
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%
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
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
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
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,
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
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
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 +
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
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
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
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
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
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 =
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
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
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
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
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
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 UnitedÂ States. Individuals are
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
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
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
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
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)
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
A government researcher examines the factors that influence a cityâ€™s crime rate. For 41 cities, she collects the crime rate (crimes per 100,000 residents), the poverty rate (in %), the median
A research analyst is trying to determine whether a firmâ€™s price-earnings (P/E) and price-sales (P/S) ratios can explain the firmâ€™s stock performance over the past year. Generally, a

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