Essential Mathematics And Statistics For Science 2nd Edition Graham Currell, Dr. Antony Dowman - Solutions

13.8 Case Studies Mini–Health Care Case Studies Nutrition Model Analysis Case Study
13.7 Autocorrelated Errors Estimation of Regressions with Autocorrelated Errors Autocorrelated Errors in Models with Lagged Dependent Variables
13.6 Heteroscedasticity
13.5 Multicollinearity
13.4 Specification Bias
13.3 Lagged Values of the Dependent Variable as Regressors
13.2 Dummy Variables and Experimental Design Experimental Design Models Public Sector Applications
13.1 Model-Building Methodology Model Specification Coefficient Estimation Model Verification Model Interpretation and Inference
12.117 You are asked to develop a multiple regression model that indicates the relationship between a person’s behavioral characteristics and the daily cost of food (daily cost). The predictor variables to be used are subject’s limiting weight (sr did lm wt), subject being a smoker (smoker),
12.116 You are asked to develop a multiple regression model that indicates the relationship between a person’s physical characteristics and the daily cost of food (daily cost). The predictor variables to be used are a doctor’s diagnosis of high blood pressure (doc bp), the ratio of waist
12.115 You are asked to develop a multiple regression model that indicates the relationship between a person’s behavioral characteristics and the quality of diet consumed as measured by the Healthy Eating Index(HEI-2005). The predictor variables to be used are whether subject limited weight (sr
12.114 You are asked to develop a multiple regression model that indicates the relationship between a person’s physical characteristics and the quality of diet consumed as measured by the Healthy Eating Index(HEI-2005). The predictor variables to be used are a doctor’s diagnosis of high blood
12.113 You have been asked to develop a model that will predict the cost with financial aid for students at highly ranked private colleges. The data file Private Colleges contains data collected by a national news service.Variables are identified in the Chapter 12 appendix.a. Specify a list of
12.112 You have been asked to develop a model that will predict the percentage of students who graduate in 4 years from highly ranked private colleges.The data file Private Colleges contains data collected by a national news service; descriptions of the predictor variables are contained in the
12.111 A group of activists in Peaceful, Montana, are seeking increased development for this pristine enclave, which has received some national recognition on the television program Four Dirty Old Men. The group claims that increased commercial and industrial development will bring new prosperity
12.110 A major real estate developer has asked you to determine the effect of the interval between house sales, and the initial house sales price on second or final sales price with adjustments for the four major U.S. market areas identified in the data set. The data on housing prices are stored in
12.109 You have been asked to develop a model that will predict home prices as a function of important economic variables. After considerable research, you locate the work of Prof. Robert Shiller, Princeton University. Shiller has compiled data for housing costs beginning in 1890. The data file
12.107 You have been hired as a consultant to analyze the salary structure of Energy Futures, Inc., a firm that produces designs for solar energy applications.The company has operated for a number of years, and in recent years there have been an increasing number of complaints that the salaries
12.106 The Center for Disease Control (CDC) is interested in knowing if there are state-level population characteristics that predict the occurrence of breast cancer death rates and the occurrence of lung cancer death rates. The data file Staten, whose variables are described in the chapter
12.105 The United Nations’ World Happiness Report aims to demonstrate the role of variables other than income in shaping peoples’ happiness. A natural candidate for such an alternative predictor of happiness at the nation level is the healthy life expectancy of the people. To find out its role,
12.104 Casper Jensen, director of energy affairs at the Ministry of Economic Affairs, wants to know whether mindset or taxes is the better instrument to stimulate the adoption of renewable energy resources to tackle climate change. He asks you to prepare an analysis investigating the relationship
12.103 An economist wishes to predict the market value of owner-occupied homes in small midwestern cities. He has collected a set of data from 45 small cities for a 2-year period and wants you to use this as the data source for the analysis. The data are in the file Citydatr the variables are
12.102 A special topic in the 2021 World Happiness Report is an attempt to quantify the effects of COVID-19. This is done by estimating a prediction model for the number of COVID-19 deaths in 2020 per 100,000 of the population. As predictors, three dummy variables are applied: being an island,
12.101 The United Nations’ World Happiness Report aims to demonstrate the role of variables other than income in determining people’s happiness. There are several candidates to build a prediction equation for happiness at the nation level: log GDP per capita, social support, healthy life
12.100 Use the data in the file Citydatr to estimate a regression equation that can be used to determine the marginal effect of the percent of commercial property on the market value per owner-occupied residence. Include the percent of owner-occupied residences, the percent of industrial property,
12.99 The Economics Department wishes to develop a multiple regression model to predict student GPA for economics courses. Department faculty have collected data for 112 graduates, which include the variables economics GPA, SAT verbal, SAT mathematics, ACT English, ACT social science, and high
12.98 The following regression model was fitted to data on 60 U.S. female amateur golfers:yn = 164,683 + 341.10x1 + 170.02x2 + 495.19x3 - 4.23x4 1100.592 1167.182 1305.482 190.02-136,040x5 - 35,549x6 + 202.52x7 125.6342 116, 2402 1106.202 R2 = .516 where yn = winnings per tournament in dollars x1 =
12.97 Based on data from 63 counties, the following model was estimated by least squares:yn = 0.58 - .052x1 - .005x2 R2 = .17 1.0192 1.0422 where yn = growth rate in real gross domestic product x1 = real income per capita x2 = average tax rate, as a proportion of gross national product The numbers
12.96 Based on data on 2,679 high school basketball players, the following model was fitted:y = b0 + b1x1 + b2x2 + g + b9x9 + e where y = minutes played in season x1 = field@goal percentage x2 = free@throw percentage x3 = rebounds per minute x4 = points per minute x5 = fouls per minute x6 = steals
12.95 Based on the 28 online purchase data, an attempt was made to explain number purchases made from an online store per hour. The model fitted was as follows:y = b0 + b1x1 + b2x2 + e where y = number of purchases per hour x1 = processing speed x2 = product quality The least squares parameter
12.94 A study was conducted to determine the factors that influencing consumer purchase intentions using 102 consumers’ feedback and obtained the following least squares model:yn = 9.958 + 4.495x1 + 2.837x2 - 2.329x3 10.2482 11.7922 10.3752 R2 = 0.5186 where yn = purchase intentions rate x1 =
12.93 A factory is estimating its yearly profit size based on several explanatory factors. Based on a sample of 55 observations, the following model was estimated by least squares:yn = 2074.838 + 29.335x1 - 14.436x2 - 7.354x3 + 45.932x4+ 5.991x5 + 1.041x6 - 2.545x7 - 0.910x8 R2 = 0.9723 where yn =
12.92 The Programme for International Student Assessment(PISA) is the OECD’s testing tool employed for measuring the ability of 15-year-olds to use their reading, mathematics, and science knowledge and skills to tackle real-life challenges. In the earlier chapters, we investigated individual
12.91 A company wants to know how effective workshops provided to the employees are. At the end of each workshop, the employees are requested to evaluate it. To assess the impact of various factors on the effectiveness ratings for each workshop, the model Y = b0 + b1X1 + b2X2 + b3X3 + e was fitted
12.90 The manager of a catering business conducted a study on the amount of preparation time (in hours)needed based on the number of dishes to be prepared and the number of servings. She uses 10 previous catering records to determine the following regression model:Y = b0 + b1X1 + b2X2 + e where Y =
12.89 A study was conducted to assess the various factors considered in a health index. A random sample of 110 adults are selected and determined the following estimated model:yn = 5.025 - 1.793x1 - 2.401x2 + 3.3759x3 + 2.953x4 10.6562 10.3942 10.7882 11.0212- 0.986x5 - 1.004x6 - 0.973x7 10.1452
12.88 [This exercise requires the material in the chapter appendix.]Suppose that the regression model y = b0 + b1x1 + b2x2 + e is estimated by least squares. Show that the residuals, ei, from the fitted model sum to 0.
12.87 A dependent variable is regressed on two independent variables. It is possible that the hypotheses H0 : b1 = 0 and H0 : b2 = 0 cannot be rejected at low significance levels, yet the hypothesis H0 : b1 = b2 = 0 can be rejected at a very low significance level. In what circumstances might this
12.86 Based on your understanding of the relation among the SSR, SSE, and SST values in a regression analysis, justify the objective and the goodness-offit of a regression model analysis.
12.85 State whether each of the following statements is true or false.a. The purpose of constructing a multiple regression is to assess whether there is a significant difference between independent variables.b. The t statistic is used to determine the significant predictors of a model.c. We can
12.84 In regression analysis, explain what information can be obtained from a regression table to help determine the regression equation and establish the relationship between the dependent and independent variables.
12.83 Explain the method of least squares discussed in this chapter. Discuss the term of least squares in this context.
12.82 A company is evaluating its sales representatives’performance. The company uses multiple regression to develop a model and identify important variables that predict every employee’s performance.Data from 36 sales representatives is collected and saved in the data file Performance. The
12.81 You are asked to develop a model to predict the change in the share of consumed energy stemming from renewable resources, using the data file Renewable Energy that contains the data for 26 European countries. The possible predictor variables are the change in the energy tax rates of
12.80 You have been asked to develop a multiple regression model to predict the traffic fatality rate per 100 million miles in 2007. The data file Vehicle Travel State contains traffic data by state for the year 2007; the variables are described in the Chapter 11 appendix.Consider the following
12.79 The following model was fitted to 47 monthly observations in an attempt to explain the difference between certificate of deposit rates and commercial paper rates:Y = b0 + b1X1 + b2X2 + e where Y = commercial paper certificate of deposit rate less commercial paper rate X1 = commercial paper
12.78 A random sample of 93 freshmen at the University of Illinois was asked to rate, on a scale of 1 (low) to 10(high), their overall opinion of residence hall life. They were also asked to rate their levels of satisfaction with roommates, with the floor, with the hall, and with the resident
12.77 In order to assess the effect in one state of a casualty insurance company’s economic power on its political power, the following model was hypothesized and fitted to data from all 50 states:Y = b0 + b1X1 + b2X2 + b3X3 + b4x4 + b5X5 + e where Y = ratio of company’s payments for state and
12.76 Consider a regression analysis with n = 49 and two potential independent variables. Suppose that one of the independent variables has a correlation of 0.56 with the dependent variable. Does this imply that this independent variable will have a very small Student’s t statistic in the
12.75 Consider a regression analysis with n = 58 and four potential independent variables. Suppose that one of the independent variables has a correlation of 0.48 with the dependent variable. Does this imply that this independent variable will have a very large Student’s t statistic in the
12.74 Consider a regression analysis with n = 34 and four potential independent variables. Suppose that one of the independent variables has a correlation of 0.23 with the dependent variable. Does this imply that this independent variable will have a very small Student’s t statistic in the
12.73 Suppose that two independent variables are included as predictor variables in a multiple regression analysis.What can you expect will be the effect on the estimated slope coefficients when these two variables have each of the given correlations?a. 0.91b. 0.38c. −0.64d. −0.11
12.72 You have been asked to develop a model to analyze salary in a large business organization.The data for this model are stored in the file named Salorg; the variable names are self-explanatory.a. Using the data in the file, develop a regression model that predicts salary as a function of the
12.71 In a survey of 27 undergraduates at the University of Illinois the accompanying results were obtained with grade point averages (y), the number of hours per week spent studying 1x12, the average number of hours spent preparing for tests 1x22, the number of hours per week spent in bars 1x32,
12.70 A regression model was estimated to compare performance of students taking a business statistics course—either as a standard 14-week course or as an intensive 3-week course. The following model was estimated from observations of 350 students (Van Scyoc and Gleason 1993):yn = -.7052 +
12.69 A consulting group offers courses in financial management for executives. At the end of these courses participants are asked to provide overall ratings of the value of the course. For a sample of 25 courses, the following regression was estimated by least squares:yn = 42.97 + 0.38x1 + 0.52x2
12.68 The following model was fitted to data on 34 states:yn = -13,878 + 570x1 + 5.01x2 - 534x3 + 30.7x4 1134.92 11.6092 1219.42 12372+ 5,787 12,8342 x5 - 2,630 11,6302 x6 R2 = 0.55 where yn = annual salary of the attorney general of the state x1 = average annual salary of lawyers, in thousands of
12.67 A business school dean wanted to assess the importance of factors that might help in predicting success in law school. For a random sample of 50 students, data were obtained when students graduated from law school, and the following model was fitted:y = a + b1x1 + b2x2 + b3x3 + e where y =
12.66 The following model was fitted to data on 32 insurance companies:yn = 7.62 - 0.16x1 + 1.23x2 R2 = 0.37 10.0082 10.4962 where yn = price-earnings ratio x1 = size of insurance company assets, in billions of dollars x2 = dummy variable taking the value 1 for regional companies and 0 for national
12.65 The following model was fitted to explain the selling prices of automobiles in a sample of 106 sales:yn = -1,205 11.032+ 45.36 14802 x1 + 3,325 14862 x2 - 1,881 19492 x3 + 3,054 17382 x4+ 1,969 17382 x5 R2 = 0.89 where yn = selling price of an automobile, in euros x1 = the size of the car x2
12.64 The following model was fitted to observations from 1972 to 1979 in an attempt to explain oil-pricing behavior:yn = 37x1 + 5.22x2 10.0292 10.502 where yn = difference between price in the current year and price in the previous year, in dollars per barrel x1 = difference between spot price in
12.63 What are the model constant and the slope coefficient of x1 when the dummy variable equals 1 in the following equations, where x1 is a continuous variable and x2 is a dummy variable with a value of 0 or 1?a. yn = 4.5 + 9.2x1 - 1.3x2 + 4.3x1x2b. yn = -6.8 + 10.4x1 + 3.5x2 - 1.8x1x2c. yn = 11.3
12.62 What is the model constant when the dummy variable equals 1 in the following equations, where x1 is a continuous variable and x2 is a dummy variable with a value of 0 or 1?a. yn = 9 + 6x1 + 9x2b. yn = 7 + 4x1 + 2x2c. yn = 4 + 4x1 + 8x2 + 9x1x2
12.61 The data file German Imports shows German real imports (y), real private consumption 1x12, and real exchange rate 1x22, in terms of U.S. dollars per mark, over a period of 22 years.Estimate the model log yt = b0 + b1 log x1t + b2 log x2t + ei and write a report on your findings.
12.60 Angelica Chandra, president of Benefits Research, Inc., has asked you to study the salary structure of her firm. Benefits Research provides consulting and management for employee health care and retirement programs. Its clients are mid- to large-sized firms. As a first step you are asked to
12.59 Consider the following nonlinear model with multiplicative errors:Y = b0Xb1 1 Xb2 2 Xb3 3 Xb4 4 e b1 + b2 = 1 b3 + b4 = 1a. Show how you would obtain the coefficient estimates.Coefficient restrictions must be satisfied.Show all your work and explain what you are doing.b. What is the constant
12.58 You have been asked to develop an exponential production function—Cobb-Douglas form—that will predict the number of microprocessors produced by a manufacturer, Y, as a function of the units of capital, X1; the units of labor, X2; and the number of computer science staff involved in basic
12.57 An agricultural economist believes that the amount of fish consumed (y) in tons in a year in the France depends on the price of fish 1x12 in euros per pound, the price of potatoes 1x22 in euros per pound, the price of chicken 1x32 in euros per pound, and the income per household 1x42 in
12.56 The following model was estimated for a sample of 322 supermarkets in large metropolitan areas(Macdonald and Nelson 1991):log1y2 = 2.921 + 0.680 log1x2 10.0772 R2 = 0.19 where y = store size x = median income in zip-code area in which store is located The number in parentheses under the
12.55 In a study of the determinants of household expenditures on vacation travel, data were obtained from a sample of 2,233 households (Hagermann 1981). The model estimated was log y = -4.035 + 1.1545 10.05442 log x1 - 0.4468 10.04562 log x2 R2 = 0.161 where y = expenditure on vacation travel x1 =
12.54 John Swanson, president of Market Research Inc., has asked you to estimate the coefficients of the model Y = b0 + b1X1 + b2X21+ b3X2 where Y is the expected sales of office supplies for a large retail distributor of office supplies, X1 is the total disposable income of residents within 5
12.53 Describe an example from your experience in which a quadratic model would be better than a linear model.
12.52 Consider the following two equations estimated using the procedures developed in this section.i. yi = 3x1.2 ii. yi = 1 + 5xi - 1.5x2i Compute values of yi when xi = 1, 2, 4, 6, 8, 10.
12.51 Consider the following two equations estimated using the procedures developed in this section:i. yi = 3x1.2 ii. yi = 3 + 5xi + 1.9 x2i Compute values of yi when xi = 1, 2, 4, 6, 8, 10.
12.50 Consider the following two equations estimated using the procedures developed in this section:i. yi = 4x1.8 ii. yi = 1 + 2xi + 2x2i Compute values of yi when xi = 1, 2, 4, 6, 8, 10.
12.49 Consider the following two equations estimated using the procedures developed in this section:i. yi = 2x1.4 ii. yi = 2 + 6xi + 1.4x2i Compute values of yi when xi = 1, 2, 4, 6, 8, 10.
12.48 Transportation Research, Inc., has asked you to prepare a multiple regression equation to estimate the effect of variables on fuel economy. The data for this study are contained in the data file Motors, and the dependent variable is miles per gallon—milpgal—as established by the
12.47 A real estate agent hypothesizes that in her town the selling price of a house in dollars (y) depends on its size in square feet of floor space 1x12, the lot size in square feet 1x22, the number of bedrooms 1x32, and the number of bathrooms 1x42. For a random sample of 20 house sales, the
12.46 An aircraft company wanted to predict the number of worker-hours necessary to finish the design of a new plane. Relevant explanatory variables were thought to be the plane’s top speed, its weight, and the number of parts it had in common with other models built by the company. A sample of
12.33 A study was conducted to determine whether certain features could be used to explain variability in the prices of furnaces. For a sample of 21 furnaces, the following regression was estimated:yn = -64.64 + 0.0011x1 10.0052+ 23.799x2 110.0562- 5.403x3 13.8332 R2 = 0.87 where y = price in euros
12.32 In a study of revenue generated by national lotteries, the following regression equation was fitted to data from 29 countries with lotteries:y = -31.323 + 0.4045x1 10.007552+ 0.8772x2 10.31072- 365.01x3 1263.882- 9.9298x4 13.45202 R2 = .51 where y = dollars of net revenue per capita per year
12.28 The following model was fitted to a sample of 30 families in order to explain household milk consumption:y = b0 + b1x1 + b2x2 + e where y = milk consumption, in quarts per week x1 = weekly income, in hundreds of dollars x2 = family size The least squares estimates of the regression parameters
12.26 The following are results from a regression model analysis:yn = -9.50 + 17.8x1 17.12+ 26.9x2 113.72- 9.2x3 13.82 R2 = 0.71 n = 39 The numbers in parentheses under the coefficients are the estimated coefficient standard errors.a. Compute two-sided 95% confidence intervals for the three
12.25 The following are results from a regression model analysis:yn = -3.54 + 7.4x1 14.22+ 3.2x2 10.72+ 10.1x3 113.22 R2 = 0.78 n = 41 The numbers in parentheses under the coefficients are the estimated coefficient standard errors.a. Compute two-sided 95% confidence intervals for the three
12.24 The following are results from a regression model analysis:yn = -3.54 + 7.4x1 11.82+ 3.2x2 11.42+ 10.1x3 14.32 R2 = 0.78 n = 41 The numbers below the coefficient estimates are the sample standard errors of the coefficient estimates.a. Compute two-sided 95% confidence intervals for the three
12.23 The results from a regression model analysis are shown as follows:yn = -61.50 + 21.8x1 12.12+ 23.7x2 122.42- 15.4x3 132.42 R2 = 0.74 n = 25 The numbers below the coefficient estimates are the sample standard errors of the coefficient estimates.a. Compute two-sided 95% confidence intervals for
12.22 Refer to the savings and loan association data given in Table 12.1.a. Estimate, by least squares, the regression of profit margin on number of offices.b. Estimate, by least squares, the regression of net revenues on number of offices.c. Estimate, by least squares, the regression of profit
12.21 The following model was fitted to a sample of 25 students using data obtained at the end of their freshman year in college. The aim was to explain students’weight gains:y = b0 + b1x1 + b2x2 + b3x3 + e where y = weight gained, in pounds, during freshman year x1 = average number of meals
12.20 The following model was fitted to a sample of 30 families in order to explain household milk consumption:y = b0 + b1x1 + b2x2 + e where y = milk consumption, in quarts per week x1 = weekly income, in hundreds of dollars x2 = family size The least squares estimates of the regression parameters
12.19 Inventas Design, an architecture company in Norway, wants to predict the number of worker-hours necessary to finish the design of a new building in Oslo.Relevant explanatory variables were thought to be the number of floors in the building, the weight of materials, and the number of parts it
12.18 A regression analysis has produced the following analysis of variance table:Analysis of Variance Source DF SS MS Regression 5 80,000 Residual error 200 15,000a. Compute se and s2e .b. Compute SST.c. Compute R2 and the adjusted coefficient of determination.Application Exercises
12.17 A regression analysis has produced the following analysis of variance table:Analysis of Variance Source DF SS MS Regression 4 40,000 Residual error 45 10,000a. Compute se and s2e.b. Compute SST.c. Compute R2 and the adjusted coefficient of determination.
12.16 A regression analysis has produced the following analysis of variance table:Analysis of Variance Source DF SS MS Regression 2 7,000 Residual error 29 2,500a. Compute se and s2e.b. Compute SST.c. Compute R2 and the adjusted coefficient of determination.
12.15 A regression analysis has produced the following analysis of variance table:Analysis of Variance Source DF SS MS Regression 8 200 Residual error 18 150a. Compute se and s2e.b. Compute SST.c. Compute R2 and the adjusted coefficient of determination.
12.14 Transportation Research, Inc., has asked you to prepare some multiple regression equations to estimate the effect of variables on vehicle horsepower.The data for this study are contained in the data file Motors, and the dependent variable is vehicle horsepower—horsepower—as established by
12.13 Transportation Research, Inc., has asked you to prepare some multiple regression equations to estimate the effect of variables on fuel economy. The data for this study are contained in the data file Motors, and the dependent variable is miles per gallon—milpgal—as established by the
12.12 Amalgamated Power, Inc., has asked you to estimate a regression equation to determine the effect of various predictor variables on the demand for electricity sales. You will prepare a series of regression estimates and discuss the results using the quarterly data for electrical sales during
12.11 Consider the following estimated linear regression equations:Y = a0 + a1X1 Y = b0 + b1X1 + b2X2a. Show in detail the coefficient estimators for a1 and b1 when the correlation between X1 and X2 is equal to 0.b. Show in detail the coefficient estimators for a1 and b1 when the correlation
12.10 Compute the coefficients b1 and b2 for the regression model yn i = b0 + b1x1i + b2x2i given the following summary statistics.a. rx1y = 0.80, rx2y = 0.30, rx1x2 = 0.90, sx1 = 500, sx2 = 400, sy = 100b. rx1y = -0.80, rx2y = -0.30, rx1x2 = 0.90, sx1 = 500, sx2 = 400, sy = 100c. rx1y = 0.40, rx2y
12.7 In a study of the influence of financial institutions on bond interest rates in Germany, quarterly data over a period of 12 years were analyzed. The postulated model was yi = b0 + b1x1i + b2x2i + ei where yi = change over the quarter in the bond interest rates x1i = change over the quarter in

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Essential Mathematics And Statistics For Science 2nd Edition Graham Currell, Dr. Antony Dowman - Solutions

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