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business statistics communicating

Business Statistics Communicating With Numbers 1st Edition Kelly Jaggia - Solutions

FILE Access the data labeled Debt Payments from the text website and estimate Debt = β 0 + β 1 Income + 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 a 95% confidence interval for expected
W ith the data in the accom panying table, estim ate GPA = β0 + β1 GRE + ε , w here GRE is a student's score on the m ath portion o f the Graduate Record Exam ination score and GPA is the student's grade p o in t average in graduate school.700 720 650 750 680 730 740 780 3.0 3.5 3.2 3.7 3.1 3.9
Using the data in the accompanying table, estimate the m odel: Salary = β 0 + β1Education + ε , where salary is measured in $ 1,000s and education refers to years o f higher education.3 4 6 2 5 4 8 0 40 53 80 42 70 50 110 38a. Construct a 90% confidence interval for the expected salary for an
Consider the following sample data:46 51 28 55 29 53 47 36 40 48 29 44 30 58 60 29 13 28 24 11 28 28 29 14a. Find the sample regression equation,ŷ= b0 + b1x1 + b2x2.b. C onstruct a 95% confidence interval fo r E(y ) if x 1 equals 50 and x2 equals 20.c. C onstruct a 95% prediction interval fo r y
Consider the following sample data:12 23 11 23 14 21 18 16 28 43 21 40 33 41 37 32a. Find the sample regression line, ŷ = b0 + b1x.b. Construct a 95% confidence interval for E(y ) if x = 15.c. Construct a 95% prediction interval fory if x = 15.
In a multiple regression with 40 observations, the following sample regression equation is obtained: ŷ = 12.8 + 2.6x1 −1 .2x2 with se = 5.84. Also, when x1 equals 15 and x2 equals 6, se(ŷ0) = 2.20.a. Construct a 95% confidence interval for E(y ) if x1 equals 15 and x2 equals 6.b. Construct a
In a simple linear regression based on 30 observations, the following information is provided: ŷ = −6.92 + 1.35x and se = 2.78. Also, se(ŷ0) evaluated a t x = 30 is 1.02.a. Construct a 95% confidence interval for E(y ) if x = 30.b. Construct a 95% prediction interval fory if x equals 30.c.
F IL E A multiple regression model is used to predict an NFL team's winning record (Win). For the explanatory variables, the average rushing yards (Rush) and the average passing yards (Pass) are used to capture offense and the average yards allowed are used to capture defense. A portion of the data
Lisa Fisher is a business school professor who would like to analyze university factors that enhance innovation. She collects data on 143 universities in 2008 for a regression where the response variable is the number of startups(Startups), which is used as a measure for innovation. Lisa believes
A financial analyst believes that the best way to predict a firm's returns is by using the firm's price-to-earnings ratio(P/E) and its price-to sales ratio (P/S) as explanatory variables.He estimates the following regression, using 30 large firms:A colleague suggests that he can improve on his
A real estate analyst estimates the following regression, relating a house price to its square footage (Sqft):In an attempt to improve the results, he adds two more explanatory variables: the number of bedrooms (Beds) and the number of bathrooms (Baths). The estimated regression equation isa.
Consider a portion of simple linear regression results,ŷ = 105.40 + 39.17x1; SSE = 407,308, n = 30 In an attempt to improve the results, two explanatory variables are added. A portion of the regression results areŷ = 4.87 + 19.47x1 − 26.31x2 + 7.31x3;SSE = 344,784, n = 30a. Formulate the
Consider the multiple linear regression model, y = β 0 +β1x1 + β2x2 + ε. Define the restricted and the unrestricted models if the hypotheses are H0.:β1 + β 2 = 1 and HA.:β 1 + β 2 ≠ 1 .
Consider the multiple linear regression model, y = β0 +β1x1 + β2x2 + β3x3 + ε. You wish to test whether the slope coefficients β1 and β3 are statistically different from each another. Define the restricted and the unrestricted models needed to conduct the test.
Considerthemultiplelinearregressionmodel,y = β0 + β1x1 +β 2x2 + β3x3 + ε . You wish to test whether the slope coefficientsβ1 and β3 are jointly significant. Define the restricted and the unrestricted models needed to conduct the test.
FIL E 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 data
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 + β1 Dshort + ε , where Dlong is the change in
F IL E A realtor examines the factors th a t influence the price o f a house in A rlington, Massachusetts. He collects data on recent house sales (Price) and notes each house's square footage (Sqft) as w ell as its num ber o f bedroom s (Beds)and num ber o f bathroom s (Baths). A portion o f the
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
A model relating the return on a firm's stock as a function of its price-to-earnings ratio and its price-to-sales ratio is estimated: Return = β 0 + β 1 P/E + β 2P/S + ε . A portion of the regression results follows.ANOVA df SS MS F Significance F Regression 2 918.7455 459.3728 2.817095
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 are as follows.ANOVA df SS MS F Significance F Regression 2
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 recordholding
The following ANOVA table was obtained when estimating a multiple regression model.ANOVA d f SS MS F Significance F Regression 2 22016.75 11008.38 0.0228 Residual 17 39286.93 2310.996 Total 19 61303.68a. How many explanatory variables were specified in the model? How many observations were used?b.
When estimating a multiple regression model based on 30 observations, the following results were obtained.Coefficients Standard Error fStat p-value Lower 95%Upper 95%Intercept 152.27 119.70 1.27 0.2142 − 93.34 397.87 X1 12.91 2.68 4.81 5.06E-05 7.40 18.41 x2 2.74 2.15 1.28 0.2128 − 1.67 7.14a.
Consider the following regression results based on 40 observations.Coefficients Standard Error f Stat p-value Lower 95%Upper 95%Intercept 43.1802 12.6963 3.4010 0.0016 17.48 68.88 X \ 0.9178 0.9350 0.9816 0.3325 − 0.97 2.81a. Specify the hypotheses to determine if the slope differs from minus
Consider the following regression results based on 20 observations.Standard Error t Stat p-value Lower 95%Upper 95%Intercept 34.2123 4.5665 7.4920 0.0000 24.62 43.81 x1 0.1223 0.1794 0.6817 0.5041 − 0.25 0.50a. Specify the hypotheses to determine if the intercept differs from zero. Perform this
In a simple linear regression based on 30 observations, it is found that b1 = 7.2 and Consider the hypotheses:H0: β1 ≥ lOandHA:β1 < 10.a. Calculate the value of the appropriate test statistic.b. At the 5% significance level, what is the critical value(s)?c. What is the conclusion to the test?
In a simple linear regression based on 25 observations, it is found that b1 = 0.5 and Consider the hypotheses:H0: β1 ≤ 0 and HA: β1, > 0.a. Calculate the value of the appropriate test statistic.b. At the 5% significance level, what is the critical value?c. What is the conclusion to the test?
In a simple linear regression based on 30 observations, it is found that b1 = 3.25 and Consider the hypotheses:H0:β 1 = 0 and HA: β 1 ≠ 0.a. Calculate the value of the appropriate test statistic.b. Approximate the p -value.c. At the 5% significance level, what is the conclusion? Is the
Describe common violations of the assumptions and offer remedies. P-96
Explain the role of the assumptions on the OLS estimators. P-96
Calculate and interpret interval estimates for predictions. P-96
Conduct a general test of linear restrictions. P-96
Conduct a test of joint significance. P-96
Conduct tests of individual significance. P-96
The following ANOVA table was obtained when estimating a multiple regression.ANOVA df SS MS F Significance F Regression 2 188246.8 94123.4 35.2 9.04E-07 Residual 17 45457.32 2673.96 Total 19 233704.1a. Calculate the standard error of the estimate. Given that the mean of the response variable is
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. P-968
In a simple linear regression based on 25 observations, the following intermediate data are given: ∑ (y i − ŷ )2 = 1,250 anda. Calculate Se2 and se. P-968b. Calculate R2.
FILE American football is the highest paying sport on a pergam e 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 regression model that links the quarterback's salary with his
FILE Education reform is one of the most hotly debated subjects on both state and national policy makers' list of socioeconomic topics. Consider a regression model that relates school expenditures and family background to student performance in Massachusetts using 224 school districts. The response
FILE A realtor in Arlington, Massachusetts, is analyzing the relationship between the sale price of a hom e (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
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 poverty
Osteoporosis is a degenerative disease that primarily affects wom en 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 = β 0 +β 1 Pop + β 2lnc + ε , where Sales refers to the sales
Consider the following sample data:52 49 45 54 45 52 40 34 11 10 9 13 9 13 6 7 25 39 25 24 31 22 28 21a. Estimate a multiple linear regression model and interpret the coefficient for x2.b. Find the predicted value for y if x1 equals 12 and x2 equals 30. P-968 Applications
In a multiple regression, the following sample regression equation is obtained:ŷ = 152 + 12.9x1 + 2.7x2.a. Predict y if x1 equals 20 and x2 equals 35.b. Interpret the slope coefficient of x1. P-968
C o n sid er th e fo llo w in g s a m p le data:x 22 24 27 21 23 14 14 15 y101 139 250 88 87 14 16 20a. C onstruct a scatterp lot and verify th a t e stim atin g a sim p le linear regression is a p p ro p ria te in this p ro b le m .b. Calculate b 0 and b1. W h a t is th e s am p le regression
C onsider th e fo llo w in g sam p le data:x 12 23 11 23 14 21 18 16 y28 43 21 40 33 41 37 32a. C onstruct a scatterp lot a nd verify th a t estim atin g a s im p le lin ear regression is a p p ro p ria te in this p ro b le m .b. Calculate b1, a n d b0. W h a t is th e s am p le regression
In a sim ple linear regression, th e fo llo w in g sam ple regression e q u a tio n is o b ta in e d :ŷ = 4 3 6 − 17x .a. In terp ret th e slope coefficient.b. P r e d ic ty i f x e q u a ls −15. P-968
In a sim ple linear regression, th e fo llo w in g sam ple regression e q u a tio n is o b tain e d :ŷ = 15 + 2.5x .a. P re d ic ty if x eq u als 10.b. W h a t happ en s to this predictio n if x doubles in value? P-968
Consider th e fo llo w in g data:a. Calculate rxy.b. Calculate b 0.c. W h a t is th e s am p le regression e q u a tio n ? Predict y if x equals - 5 . P-968
In a s im p le lin ear regression, th e fo llo w in g in fo rm a tio n is given:a. Calculate b1.b. Calculate b0.c. W h a t is th e s am p le regression e q u a tio n ? P redict y if x e q u a ls - 2 0 . P-968
In a sim ple linear regression, th e fo llo w in g in form atio n is given:a. Calculate b1.b. Calculate b 0.c. W h a t is th e s am p le regression eq u a tio n ? P red ict y if x equals 40. P-968
F I L E The fo llo w in g ta b le lists th e N ational Basketball Association's leading scorers, their average points per gam e(PPG), and their average m inutes per g am e (MPG) for 2008;th e data are also available on th e te xt w ebsite, labeled Points.PPG MPG D. Wade 30.2 38.6 L. James 28.4 37.7
F IL E M any attem pts have been m ad e to relate happiness w ith various factors. O ne such study relates happiness w ith age and finds th a t holding everything else constant, people are least happy w h en they are in th eir m id-40s (The E conom ist, D ec e m b e r 1 6 , 2 0 1 0 ). T h e a cc o
A realto r studies th e relatio n sh ip b e tw e e n th e size o f a house(in square feet) and th e prop erty taxes o w ed by th e owner.He collects th e follow ing data on six hom es in an affluent su b u rb 6 0 m iles o u tsid e o f N e w York City. P-968 Square Feet Property Taxes ($)Home 1
F I L E D iv e rs ific a tio n is c o n s id e re d im p o r t a n t in fin a n c e because it allo w s investors to red uce risk by investing in a v a r ie ty o f assets. It is e s p e c ia lly e ffe c tiv e w h e n th e c o rre la tio n b e tw e e n th e assets is lo w . C o n s id er th e a cc o
In June 2 0 0 9 an onslaught o f m iserable w e a th e r in N ew England played havoc w ith people's plans and psyches.How ever, th e dreary w e a th e r b ro u g h t a q u iet benefit to m an y city neighborhoods. Police reported th a t th e w e a th e r was a key factor in reducing fatal and no
A sam ple o f 25 observations provides th e follow ing statistics:sx = 2 , sy = 5, and sxy = − 1.75a. Calculate and in terpret th e sam ple correlation coefficient rxy.b. Specify th e co m p etin g hypotheses in order to d eterm in e w h eth er th e po pulation correlation coefficient differs
A sam ple o f 10 observations provides th e follow ing statistics:sx = 13, sy = 18, a n d sxy= 117.22a. Calculate and in terpret th e sam ple correlation coefficient rxy.b. Specify th e hypo th eses to d e te rm in e w h e th e r th e p o p u la tio n correlation coeffic ie n t is positive.c. C
Consider the following com peting hypotheses:Th e s am p le consists o f 3 0 ob se rva tio n s a nd th e sam ple co rrelation c o e ffic ie n t is - 0 . 6 0 .a. C alcu late th e v alu e o f th e test statistic.b. A pproxim ate th e p -value.c. At t h e 5 % significance level, w h a t is th e
C onsid er th e fo llo w in g c o m p e tin g hypotheses:The sample consists of 25 observations and the sample correlation coefficient is 0.15.a. Calculate the value o f the test statistic.b. At the 5% significance level, specify the critical value(s)and the decision rule.c. W hat is the conclusion
Consider th e follow ing sam ple data:x- 3 0 10 0 23 16 y44 -1 5 -1 0 - 2 5a. Construct and in terpret a scatterplot.b. Calculate and in terpret sxy.c. C alcu late a nd in te rp re t rxy. P-968
Consider the following sample data:x 8 5 3 10 2 y380 210 90 20 2a. Construct and in terpret a scatterplot.b. Calculate and interpret th e sam ple covariance.c. C alcu late and in terp re t th e sam p le correlation coefficient. P-968
Differentiate between R2 and adjusted R. P-968
Calculate and interpret the coefficient of determination R. P-968
Calculate and interpret the standard error of the estimate. P-968
Estimate the multiple linear regression model and interpret the coefficients. P-968
Estimate the simple linear regression model and interpret the coefficients. P-968
Discuss the limitations of correlation analysis. P-968
Conduct a hypothesis test for the population correlation coefficient. P-968
Calculate the sample covariance and the sample correlation coefficient between debt payments and income from the data in Table 14.1. Interpret these values.
Use Excel to recalculate the sample covariance and the sample correlation coefficient between debt payments and income from the data in Table 14.1.
Using the critical value approach to hypothesis testing, determine whether the correlation coefficient between income and debt payments is significant at the 5% level.
Using the data from Table 14.1, let debt payments represent the response variable and income represent the explanatory variable.a. Calculate and interpret b 1.b. Calculate and interpret b0.c. What is the sample regression equation?d. Predict debt payments if income is $80,000.
Given the data from Table 14.1, use Excel to re-estimate the sample regression equation with debt payments as the response variable and income as the explanatory variable.
a. Given the data from Table 14.1, estimate the multiple regression model with debt payments as the response variable and income and the unemployment rate as the explanatory variables.b. Interpret the regression coefficients.c. Predict debt payments if income is $80,000 and the unemployment rate is
Consider the sample data in Table 14.1 and the regression output for Model 1 in Table 14.4. Use the sample regression equation, Income, to calculate and interpret the standard error of the estimate se.
Calculate and interpret the coefficient of determination R2 given the sample data in Table 14,1 and the sample regression equation from Model 1:10.44Income.
Using the regression statistics from Table 14.7, what is the sample correlation coefficient between y and ŷ for Model 2? Square this value to compute R2.
Using the regression statistics from Table 14.7, use the value of the adjusted R2 for model comparison.
Interpret the resulting coefficient of determination.
Estimate and interpret a multiple regression model where the asking price is the response variable and the above four factors are the explanatory variables.
Provide summary statistics on the asking price, square footage, the number of bedrooms, the number of bathrooms, and the lot size.
Make an investment recommendation for Minori.
Discuss the statistical significance of the correlation coefficients.
Calculate and interpret the sample correlation coefficient of each fund with Magellan.
F I L E 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 data can be found on the text website, labeled Hourly Wage.a. Estimate: Wage = β 0 + β1 EDUC + β
FILE 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 in 2008
FILE 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
F ILE 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. A P/E ratio is calculated as a firm's share price compared to the income or profit earned by the firm per share. Generally,
FILE The homeownership rate in the U.S. was 67.4% in 2009. In order to determine if homeownership is linked with income, 2009 state level data on homeownership rate (Ownership) and median household income (Income)were collected. A portion of the data is shown below; the complete data can be found
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 following table shows the annual returns for two of Vanguard's mutual funds: the Vanguard Energy Fund and the Vanguard Healthcare Fund.Annual Total Returns (in percent)Year Energy x Healthcare y 2004 36.65 9.51 2005 44.60 15.41 2006 19.68 10.87 2007 37.00 4.43 2008 -42.87 − 18.45 sx = 35.77
FILE 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 cap
FILE 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 made, and the average number of yards allowed during the 2009 NFL season. The complete data, labeled Football, can be found on the text
A financial analyst uses the follow ing m odel to estim ate a firm's stock return: Return = β 0 + β 1 P/E + β 2P/S + ε , where P/E is a firm's price-to-earnings ratio and P/S is a firm's priceto-sales ratio. A portion o f the regression results is shown.ANOVA df SS MS F Significance F
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 are shown.ANOVA df SS MS F Significance F Regression 2 3549788
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 tw o models:Model 1. College GPA = β0 + β1 High School GPA + εModel 2. College GPA = β0
The following ANOVA table was obtained when estimating a multiple regression.ANOVA df SS MS F Significance F Regression 2 188246.8 94123.4 35.2 9.04E-07 Residual 17 45457.32 2673.96 Total 19 233704.1a. Calculate the standard error of the estimate. Given that the mean of the response variable is
The following ANOVA table was obtained when estimating a multiple linear regression.ANOVA d f SS MS F Significance F Regression 2 161478.4 80739.19 11.5854 0.0002 Residual 27 188163.9 6969.03 Total 29 349642.2a. Calculate the standard error of the estimate. Given that the mean of the response

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