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

12.5 Given the following estimated linear model yn = 10 - 2x1 - 14x2 + 6x3a. What is the change in yn when x1 increases by 4?b. What is the change in yn when x3 decreases by 1?c. What is the change in yn when x2 decreases by 2?Application Exercises
12.4 Given the following estimated linear model yn = 10 + 2x1 + 12x2 + 8x3a. What is the change in yn when x1 increases by 4?b. What is the change in yn when x3 increases by 1?c. What is the change in yn when x2 increases by 2?
12.3 Given the estimated linear model yn = 10 + 2x1 + 12x2 + 8x3a. Compute yn when x1 = 20, x2 = 11, x3 = 10.b. Compute yn when x1 = 15, x2 = 24, x3 = 20.c. Compute yn when x1 = 20, x2 = 19, x3 = 25.d. Compute yn when x1 = 10, x2 = 9, x3 = 30.
12.2 Given the estimated linear model yn = 10 + 5x1 + 4x2 + 2x3a. Compute yn when x1 = 20, x2 = 11, and x3 = 10.b. Compute yn when x1 = 15, x2 = 14, and x3 = 20.c. Compute yn when x1 = 35, x2 = 19, and x3 = 25.d. Compute yn when x1 = 10, x2 = 17, and x3 = 30.
12.1 Given the estimated linear model yn = 12 + 5x1 + 6x2 + 2x3a. Compute yn when x1 = 11, x2 = 24, and x3 = 27.b. Compute yn when x1 = 31, x2 = 20, and x3 = 17.c. Compute yn when x1 = 32, x2 = 29, and x3 = 13.d. Compute yn when x1 = 30, x2 = 26, and x3 = 9.
12.10 Case Study Projects Mini Case Studies Nutrition Based Mini-Case Studies Automobile Fuel Case Study Project
12.8 Dummy Variables for Regression Models Differences in Slope
12.7 Transformations for Nonlinear Regression Models Quadratic Transformations Logarithmic Transformations
12.6 Prediction
12.4 Confidence Intervals and Hypothesis Tests for Individual Regression Coefficients Confidence Intervals Tests of Hypotheses
12.3 Explanatory Power of a Multiple Regression Equation
12.2 Estimation of Coefficients Least Squares Procedure
12.1 The Multiple Regression Model Model Specification Model Objectives Model Development Three-Dimensional Graphing
11.100 In recent news commentaries, it has been argued that the quality of family life has decayed in recent years. Arguments include statements that families do not share meals together. Because of busy schedules, families just go out to eat because there is limited time for food preparation. What
11.99 A number of nutritionists have argued that fastfood restaurants have a negative effect on nutrition quality. In this exercise you are asked to determine if there is evidence to conclude that increasing the number of meals at fast-food restaurants will have a negative effect on diet quality.
11.98 A group of social workers who work with lowincome people have argued that the poverty income ratio is directly related to the quality of an individual person’s diet. That is, people with higher ratios will be more likely to have higher-quality diets, and those with lower ratios will have
11.92 The United Nations’ World Happiness Report aims to demonstrate the role of variables other than income in shaping peoples’ happiness. Let us consider the role of GDP, our income measure. Investigate the relationship between LogGDPperCapita and Life-Ladder for 2021 in the data file
11.85 Casper Jensen, director of energy affairs at the Ministry of Economic Affairs, wants to know whether mindset or taxes are 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
11.78 Based on a sample of 18 observations, the population regression model yi = b0 + b1xi + ei was estimated. The least squares estimates obtained were as follows:b0 = 5 and b1 = 2.2 The total and error sums of squares were as follows:SST = 78 and SSE = 49a. Find and interpret the coefficient of
11.77 Based on a sample of 45 observations, the population regression model yi = b0 + b1xi + ei was estimated. The least squares estimates obtained were as follows:b0 = 60 and b1 = 15 The regression and error sums of squares were as follows:SSR = 254 and SSE = 103a. Find and interpret the
11.73 Based on a sample on n observations, 1x1, y12, 1x2, y22,c, 1xn, yn2, the sample regression of y on x is calculated. Show that the sample regression line passes through the point 1x = x, y = y2, where x and y are the sample means.
11.71 For a random sample of 350 industries, the sample correlation between the proportion of an industry’s employee turnover rate and economic growth rate was found to be 0.8729. Test, against a two-sided alternative, the null hypothesis that the population correlation is 1 at 1% significance
11.70 For a random sample of 53 building supply stores in a chain, the correlation between annual sales per square meter of floor space and annual rent per square meter of floor space was found to be 0.37. Test the null hypothesis that these two quantities are uncorrelated in the population against
11.69 Josie Foster, president of Public Research, Inc., has asked for your assistance in a study of the occurrence of crimes in different states before and after a large federal government expenditure to reduce crime. As part of this study she wants to know if the crime rate for selected crimes
11.68 Frank Anscombe, senior research executive, has asked you to analyze the following four linear models using data contained in the data file Anscombe:Y1 = b0 + b1X1 Y2 = b0 + b1X2 Y3 = b0 + b1X3 Y4 = b0 + b1X4 Use your computer package to obtain a linear regression estimate for each model.
11.67 In the commodity price file of the World Bank, two different types of coffee are enclosed: Arabica and Robusta. Their price progressions differ, but the differences are not significant. There is also a third category, consisting of a mix of the two coffee types. To create a balanced mix, we
11.61 A college administers a student evaluation questionnaire for all its courses. For a random sample of 12 courses, the accompanying table and the data file Student Evaluation show both the average student ratings of the instructor (on a scale of 1 to 5), and the average expected grades of the
11.59 The sample correlation for 68 pairs of annual returns on common stocks in country A and country B was found to be 0.51. Test the null hypothesis that the population correlation is 0 against the alternative that it is positive.It is recommended that the following exercises be solved by using a
11.58 For a random sample of 353 high school teachers, the correlation between annual raises and teaching evaluations was found to be 0.11. Test the null hypothesis that these quantities are uncorrelated in the population against the alternative that the population correlation is positive.
11.56 An instructor in a statistics course set a final examination and also required the students to do a data analysis project. For a random sample of 10 students, the scores obtained are shown in the table. Find the sample correlation between the examination and project scores.Examination 81 62
11.55 Using a 0.10 level of significance, test the null hypothesis H0 : r = 0 versus H1 : r ? 0 given the following.a. A sample correlation of 0.46 for a random sample of size n = 25.b. A sample correlation of 0.52 for a random sample of size n = 45.c. A sample correlation of 0.16 for a random
11.54 Given the following pairs of 1x, y2 observations, compute the sample correlation.a. 12, 52, 15, 82, 13, 72, 11, 22, 18, 152b. 17, 52, 110, 82, 18, 72, 16, 22, 113, 152c. 112, 42, 115, 62, 116, 52, 121, 82, 114, 62d. 12, 82, 15, 122, 13, 142, 11, 92, 18, 222
11.51 The data file Trading Stocks shows percentage changes (xi) in a stock market over the first five trading days of each of 11 years and also the corresponding percentage changes (yi) in the index over the whole year. If the stock market increases by 3.0% in the first five trading days of a
11.50 A liquor wholesaler is interested in assessing the effect of the price of a premium scotch whiskey on the quantity sold. The results in the accompanying table on price, in dollars, and sales, in cases, were obtained from a sample of 8 weeks of sales records.Price 19.2 20.5 19.7 21.3 20.8 19.9
11.49 For a sample of 50 monthly observations the regression of the percentage return on an investment (y)against the percentage change in the consumer price index (x) was estimated. The sample regression line, obtained through least squares, is as follows:y = -0.003 + 8.2x The estimated standard
11.48 It was hypothesized that the number of bottles of craft beer sold per evening in the restaurants of a city depends linearly on the average costs of meals in the restaurants.The following results were obtained for a sample of n = 17 restaurants, of approximately equal size, where y = number of
11.45 For a sample of 20 monthly observations, a financial analyst wants to regress the percentage rate of return(Y) of the common stock of a corporation on the percentage rate of return (X) of the Standard & Poor’s 500 index. The following information is available:a 20 i=1 yi = 22.6 a 20 i=1 xi
11.44 Doctors are interested in the relationship between the dosage of a medicine and the time required for a patient’s recovery. The following table shows, for a sample of 10 patients, dosage levels (in grams) and recovery times (in hours). These patients have similar characteristics except for
11.43 A sample of 10 blue-collar employees at a production plant was taken. Each employee was asked to assess their job satisfaction (x) on a scale of 1 to 10. In addition, the numbers of days absent (y) from work during the last year were found for these employees. The sample regression line yn i
11.42 Given a simple regression analysis, suppose that we have obtained a fitted regression model yn i = 8 + 10xi and also se = 11.23 x = 8 n = 44 a ni=1 1xi - x22 = 800 Find the 95% confidence interval and 95% prediction interval for the point where x = 17.Application Exercises
11.40 Given a simple regression analysis, suppose that we have obtained a fitted regression model yn i = 14 + 7xi and also se = 7.45 x = 8 n = 25 a ni=1 1xi - x22 = 300 Find the 95% confidence interval and 95% prediction interval for the point where x = 11.
11.38 Estimate a linear regression model for the monthly rents of student rooms in Amsterdam on room size, using the data file Amsterdam Rents.a. Use an unbiased estimation procedure to obtain a point estimate of the variance of the error terms in the population regression.b. Use an unbiased
11.29 Find and interpret the coefficient of determination for the regression of the percentage change in the stock market index in a year based on the percentage change in the index over the first five trading days of the year. Compare your answer with the sample correlation found for these data.
11.28 Find and interpret the coefficient of determination for the regression of DVD system sales on price, using the following data.Sales 420 380 350 400 440 380 450 420 Price 98 194 244 207 89 261 149 198
11.19 A company sets different prices for a particular DVD system in eight different regions of the country. The accompanying table shows the numbers of units sold and the corresponding prices (in dollars).Sales 420 380 350 400 440 380 450 420 Price 104 195 148 204 96 256 141 109a. Graph these
11.18 Compute the coefficients for a least squares regression equation and write the equation, given the following sample statistics.a. x = 10, y = 50, SX = 80, SY = 75, RXY = 0.4, n = 60b. x = 60, y = 50, SX = 80, SY = 65, RXY = 0.7, n = 60c. x = 90, y = 100, SX = 60, SY = 70, RXY = 0.4, n = 60d.
11.15 Explain the difference between the residual ei and the model error ei.
11.13 An agent for a real estate company in a large European city collected data, as shown in the following table, on the sizes (x in square feet) and monthly rents (y in euros)of a sample of eight apartments in a neighborhood.Monthly Rent (€) 900 1500 825 1600 2000 950 1750 1400 Size (square
11.12 As the new market manger for Blue Crunchies breakfast cereal, you are asked to estimate the demand for next month using regression analysis. Two months ago the target market had 20,000 families and sales were 3,780 boxes and, 1 month ago the target market was 40,000 families and sales were
11.5 Simoné Berk, president of Food Unlimited, has asked you to study the relationship between market price(euros) and the amount of rice (kg) supplied by her competitor, Good Food, Inc. Simoné supplies you with the following observations, of price per kg and number of kgs, obtained from the
11.1 Complete the following for the 1x, y2 pairs of data points (3,1), (4,5), (5,4), (7, 6), and (9, 8).a. Prepare a scatter plot of these data points.b. Compute b1.c. Compute b0.d. What is the equation of the regression line?
11.9 Graphical Analysis
11.8 Beta Measure of Financial Risk
11.7 Correlation Analysis Hypothesis Test for Correlation
11.6 Prediction
11.3 Least Squares Coefficient Estimators Computer Computation of Regression Coefficients
10.58 We will now understand the effects of another home condition: does the student have books at home to help with their school work? Using a random sample of 500 observations from the PISA database, to be found in the data file PISA Sample, analyze the difference in means of the mathematics and
10.57 Let us now investigate the effects of another home condition: does the student have access to the Internet at home? Using a random sample of 500 observations from the PISA database, to be found in the data file PISA Sample, analyze the difference in means of the mathematics and reading scores
10.56 Let us now investigate another home condition:can the student use educational software at home?Using a random sample of 500 observations from the PISA database, to be found in the data file PISA Sample, analyze the difference in means of the mathematics and reading scores between students who
10.55 Let us look at another home condition in this exercise:does the student have a computer for school work at home? Using a random sample of 500 observations from the PISA database, to be found in the data file PISA Sample, analyze the difference in means of the mathematics and reading scores of
10.54 In this exercise, let us look at a third home condition that might affect the reading and mathematics scores of 15-year-old students: does the student have a quiet place to study at home? Using a random sample of 500 observations from the PISA database, to be found in the data file PISA
10.53 In this exercise, we will be looking at another home condition that might affect the mathematics and readings scores of 15-year-old students: does the student have a room of their own at home? Using a random sample of 500 observations from the PISA database, to be found in the data file PISA
10.48 Mortgage banks in a European country are very competitive, with institutions competing over market shares. As a local branch manager of Bank H, you are competing with the local branches of Bank S and Bank N. The data file Mortgage Banks contains the year-on-year growth rates of issued
10.47 You are the product manager for brand 4 in a large food company. The company president has complained that a competing brand, called brand 2, has higher average sales. The data services group has stored the latest product sales (saleb2 and saleb4) and price data (apriceb2 and apriceb4) in a
10.45 Most retail outlets like H&M, Zara, and Forever21 have an end-of-season sale in December every year.Suppose the manager of a retail chain in Arezzo, Italy, wants to know the sales for two outlets and determine the difference in sales between them. The sales report showed that outlet 1 located
10.44 The COVID-19 pandemic has significantly affected the real estate market in a country where there was a large decline in demand and nationwide home prices dropped to their lowest. To study the impact of the pandemic, a real estate company randomly selected 15 residential units’ prices (in $
10.43 Let us analyze if differences exist in the 2020 scores for SocialSupport, FreedomToMakeLifeChoices, and PerceptionsOfCorruption between African nations (Sub-Saharan Africa and North Africa together) and American nations (Latin America and Caribbean and North America together). Using the data
10.42 We will now investigate if differences exist in the 2020 scores for LadderChange, PosAffectChange, and NegAffectChange between African nations and American nations (taking the northern and southern regions together for both continents). Using the data file Happiness Report Data, prepare a
10.36 Independent random samples of patients who had received knee and hip replacement were asked to assess the quality of service on a scale from 1 (low) to 7 (high). For a sample of 83 knee patients, the mean rating was 6.543 and the sample standard deviation was 0.649. For a sample of 54 hip
10.35 A survey was conducted to determine the difference between the annual salaries of employees with and without a college degree. For a sample of 115 employees with a college degree, the mean salary per year was£45,248, and the sample standard deviation was £10,974.For a sample of 102
10.28 Researchers test the null hypothesis that the proportion of three-year-old children receiving their initial formal education in an urban location is the same as the proportion of those in a rural location. Based on sample data, the null hypothesis is rejected at the 10% significance level.
10.27 A university research team was studying the relationship between idea generation by groups with and without a moderator. For a random sample of four groups with a moderator, the mean number of ideas generated per group was 78.0, and the standard deviation was 24.4. For a random sample of four
10.26 A publisher is interested in the effects on sales of college texts that include more than 100 data files. The publisher plans to produce 20 texts in the business area and randomly chooses 10 to have more than 100 data files. The remaining 10 are produced with at most 100 data files. For those
10.25 To evaluate if auditors might be helped in determining the chances of fraud if they carefully measure cash flow, samples of midlevel auditors from CPA firms were asked to indicate the chance of material fraud on a scale from 0 to 100 for a case. A random sample of 32 auditors used the
10.24 It is hypothesized that the total sales of a corporation should vary more in an industry with active price competition than in one with duopoly and tacit collusion.In a study of the merchant ship production industry it was found that in 4 years of active price competition, the variance of
10.23 A professor claims that exam scores for non-accounting majors are more variable than for accounting majors.Random samples of 30 non-accounting majors and 30 accounting majors are taken from a final exam. Test at the 1% level the null hypothesis that the two population variances are equal
10.22 Test the hypothesis H0 : s2x= s2y H1 : s2x 7 s2y using the following data.a. s2x= 125, ny = 45; s2y= 51, ny = 41b. s2x= 125, ny = 45; s2y= 235, ny = 44c. s2x= 134, ny = 48; s2y= 51, ny = 41d. s2x= 88, ny = 39; s2y= 167, ny = 25
10.21 Of a random sample of 1,000 people in Denmark, 500 had a positive attitude toward TV salespeople. Of an independent random sample of 1,600 people in France, 730 had a positive attitude toward TV salespeople.Test, at the 10% level, the null hypothesis that the population proportions are equal,
10.19 Of a random sample of 455 high-quality investment equity options, 203 had less than 30% debt. Of an independent random sample of 205 high-risk investment equity options, 183 had less than 30% debt. Test, against a two-sided alternative, the null hypothesis that the two population proportions
10.18 Employees of a building materials chain in Monaco who were facing a shutdown were surveyed on a prospective employee ownership plan. Some employees pledged €10,000 to this plan, putting up €1,000 immediately, while others indicated that they did not intend to pledge. Of a random sample of
10.17 Small-business telephone users were surveyed 6 months after access to carriers other than Carrier A became available for wide-area telephone service.Of a random sample of 240 Carrier A users, 133 said they were attempting to learn more about their options, as did 201 of an independent random
10.15 Random samples of 900 people in the United States and in Great Britain indicated that 60% of the people in the United States were positive about the future economy, whereas 66% of the people in Great Britain were positive about the future economy. Does this provide strong evidence that the
10.8 A screening procedure was designed to measure attitudes toward minorities as managers. High scores indicate negative attitudes and low scores indicate positive attitudes. Independent random samples were taken of 151 male financial analysts and 108 female financial analysts. For the former
10.7 You have been asked to determine if two different production processes have different mean numbers of units produced per hour. Process 1 has a mean defined as m1 and process 2 has a mean defined as m2.The null and alternative hypotheses are as follows:H0 : m1 - m2 … 0 H1 : m1 - m2 7 0 The
10.6 You have been asked to determine if two different production processes have different mean numbers of units produced per hour. Process 1 has a mean defined as m1 and process 2 has a mean defined as m2.The null and alternative hypotheses are as follows:H0 : m1 - m2 = 0 H1 : m1 - m2 7 0 Use a
10.4 You have been asked to conduct a national study of urban home selling prices to determine if there has been an increase in selling prices over time. There has been some concern that housing prices in major urban areas have not kept up with inflation over time. Your study will use data
10.3 In a study comparing banks in two countries, a sample of 148 matched pairs of banks was formed. Each pair contained one bank from the Netherlands and one from Croatia. The pairings were made in such a way that the two members were as similar as possible in regard to such factors as size and
10.4 Tests of the Equality of the Variances Between Two Normally Distributed Populations 10.5 Some Comments on Hypothesis Testing
10.3 Tests of the Difference Between Two Population Proportions(Large Samples)
10.2 Tests of the Difference Between Two Normal Population Means:Independent Samples Two Means, Independent Samples, Known Population Variances Two Means, Independent Samples, Unknown Population Variances Assumed to Be Equal Two Means, Independent Samples, Unknown Population Variances Not Assumed
10.1 Tests of the Difference Between Two Normal Population Means:Dependent Samples Two Means, Matched Pairs
9.78 The ICU data file contains information from a study conducted on adult patients that were admitted to the Intensive Care Unit (ICU) of a hospital.Variable descriptions are located in the chapter appendix. Patients with heart rate higher than 120 bpm are labeled as “in danger patients” and
9.77 The ICU data file contains information of a study made with adult patients that were admitted to the Intensive Care Unit (ICU) of a hospital.Variable descriptions are located in the chapter appendix. It is known that patients with a heart rate higher than 120 bpm are more likely to suffer
9.72 A study at the hospital in Finland concluded that the percentage of patients admitted with a bone fracture was less than 15%. State whether the conclusions of the study are still valid. You are then asked to restrict your study to patients above the age of 50 years who were admitted with a
9.71 A police officer is analyzing the crime index of a town in a region. He claims that the town has an average crime index of 45.25 with the population standard deviation being no more than 10. A random sample of 14 towns’ crime index provides the followings measures a8 i=1 xi = 560 and a 8i=1
9.70 When operating normally, a manufacturing process produces sheets of paper for which the mean weight of the active ingredient is 5 grams, and the standard deviation is 0.025 gram. For a random sample of 12 sheets the following weights of active ingredient (in grams) were found:4.97 5.00 4.98
9.66 The World Happiness Report is an annual UN Sustainable Development Solutions Network publication. The first of this was published in 2011, in line with the Bhutanese Resolution passed by the UN General Assembly in June 2011 that invited national governments to “give more importance to
9.65 Lantmännen Cerealia, Stockholm, has asked you to study the variability of the weights of cereal bags produced in plant 2, located in Norway. The package weights are known to be normally distributed. Using a random sample of n = 125, you find that the sample mean weight is 40.9 and the sample
9.54 Carefully explain what is meant by the p-value of a test, and discuss the use of this concept in hypothesis testing.
9.53 Based on your understanding of each of the following pairs of terms, provide an example to differentiate them.a. Null and alternative hypothesesb. Simple and composite hypothesesc. One-sided and two-sided alternativesd. Type I and Type II errorse. Significance level and (1 – power)

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

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