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Introduction To The Practice Of Statistics 6th Edition David S. Moore, George P. McCabe, Bruce A. Craig - Solutions
Finding a multiple regression model on the Internet. Search the Internet to find an example of the use of multiple regression. Give the setting of the example, describe the data, give the model, and
The final multiple regression model of Taste.Use the three explanatory variables Acetic, H2S, and Lactic in a multiple regression to predict Taste. Write a short summary of your results, including an
Another multiple regression model of Taste.Carry out a multiple regression using H2S and Lactic to predict Taste. Comparing the results of this analysis with the simple linear regressions using each
Multiple regression model of Taste. Carry out a multiple regression using Acetic and H2S to predict Taste. Summarize the results of your analysis. Compare the statistical significance of Acetic in
Comparing the simple linear regression models. Compare the results of the regressions performed in the three previous exercises.Construct a table with values of the F statistic, its P-value, R2, and
The final simple linear regression model of Taste. Repeat the analysis of Exercise 11.53 using Taste as the response variable and Lactic as the explanatory variable.
Another simple linear regression model of Taste. Repeat the analysis of Exercise 11.53 using Taste as the response variable and H2S as the explanatory variable.
Simple linear regression model of Taste.Perform a simple linear regression analysis using Taste as the response variable and Acetic as the explanatory variable. Be sure to examine the residuals
Pairwise scatterplots of the explanatory variables. Make a scatterplot for each pair of variables in the CHEESE data set (you will have six plots). Describe the relationships. Calculate the
Describing the explanatory variables. For each of the four variables in the CHEESE data set, find the mean, median, standard deviation, and interquartile range. Display each distribution by means of
Interpretation of coefficients in log PCB regressions. Use the results of your analysis of the log PCB data in Exercise 11.48 to write an explanation of how regression coefficients, standard errors
CH ALLENGE Predicting total TEQ using transformed variables. Use the log data set that you created in Exercise 11.46 to find a good multiple regression model for predicting the log of TEQ.Use only
CH ALLENGE Even more on predicting total amount of PCB using transformed variables. Use the log data set that you created in Exercise 11.46 to find a good multiple regression model for predicting the
CH ALLENGE Predicting total amount of PCB using transformed variables, continued. Refer to the previous exercise.(a) Use numerical and graphical summaries to describe the relationships between each
CHALLENGE Predicting total amount of PCB using transformed variables. Because distributions of variables such as PCB, the PCB congeners, and TEQ tend to be skewed, researchers frequently analyze the
CHALLENGE Multiple regression model for total TEQ, continued. The information summarized in TEQ is used to assess and manage risks from these chemicals. For example, theWorld Health Organization
Multiple regression model for total TEQ.Dioxins and furans are other classes of chemicals that can cause undesirable health effects similar to those caused by PCB. The three types of chemicals are
More on predicting the total amount of PCB.Run a regression to predict PCB using the variables PCB52, PCB118, and PCB138. Note that this is similar to the analysis that you did in Exercise 11.41,
Adjusting analysis for potential outliers. The examination of the residuals in part (c) of the previous exercise suggests that there may be two outliers, one with a high residual and one with a low
Predicting the total amount of PCB. Use the four congeners, PCB52, PCB118, PCB138, and PCB180, in a multiple regression to predict PCB.(a) Write the statistical model for this analysis.Include all
Relationship among PCB congeners. Production of polychlorinated biphenyls (PCBs) was banned in the United States in 1977, but because of their widespread use, these compounds are found in many
CHALL ENGE Predicting bone resorption using transformed variables. Refer to the previous exercise. Rerun using logs.The following eleven exercises use the PCB data set described in the Data Appendix.
CHALL ENG E Predicting bone resorption. Refer to Exercises 11.34 to 11.36. Answer these questions with the roles of VO+ and VO− reversed;that is, run models to predict VO−, with VO+ as an
CHALL ENGE Predicting bone formation using transformed variables. Because the distributions of VO+, VO−, OC, and TRAP tend to be skewed, it is common to work with logarithms rather than the
More on predicting bone formation. Now consider a regression model for predicting VO+using OC, TRAP, and VO−.(a) Write out the statistical model for this analysis including all assumptions.(b) Run
Predicting bone formation. Let’s use regression methods to predict VO+, the measure of bone formation.(a) Since OC is a biomarker of bone formation, we start with a simple linear regression using
Bone formation and resorption. Consider the following four variables: VO+, a measure of bone formation; VO−, a measure of bone resorption;OC, a biomarker of bone formation; and TRAP, a biomarker of
Selecting from among several models. Refer to the results from the previous exercise.(a) Make a table giving the estimated regression coefficients, standard errors, t statistics, and P-values.(b)
Building a multiple linear regression model.Let’s now build a model to predict the lifesatisfaction score, LSI.(a) Consider a simple linear regression using GINI as the explanatory variable. Run
Predicting a nation’s “average happiness”score. Consider the following five variables for each nation: LSI, life-satisfaction score, an index of happiness; GINI, a measure of inequality in the
Predicting GPA of seventh-graders. Refer to the educational data for 78 seventh-grade students given in Table 1.9 (page 29). We view GPA as the response variable. IQ, gender, and self-concept are the
Multiple linear regression model. Now consider a regression model using all three explanatory variables.(a) Write out the statistical model for this analysis, making sure to specify all
Looking at the simple linear regressions.Now let’s look at the relationship between each explanatory variable and the total score.(a) Generate scatterplots for each explanatory variable and the
Annual ranking of world universities. Let’s consider developing a model to predict total score based on the peer review score (PEER), faculty-tostudent ratio (FtoS), and citations-to-faculty
Interpretation of coefficients in a multiple regression. Recall that the relationship between an explanatory variable and a response variable can depend on what other explanatory variables are
Transforming the variables. Sometimes we attempt to model curved relationships by transforming variables. Take the logarithm of assets and the logarithm of the number of accounts. Does the
Curvilinear relationship versus a couple of outliers. To one person, the plot of assets versus the number of accounts indicates that the relationship is curved. Another person might see this as a
Adjusting for correlated explanatory variables.In the multiple regression you performed in the previous exercise, the P-value for the number of accounts was 0.8531, while the P-value for the square
Online stock trading. Online stock trading has increased dramatically during the past several years. An article discussing this new method of investing provided data on the major Internet stock
Even more on nutrition labels for foods.Refer to the previous two exercises. When the researchers planned these studies, they expected both unfavorable nutrients and favorable nutrients to be
More on nutrition labels for foods. The product used in the previous exercise was described by the researchers as a poor-nutrition product.The label information for this product had high values for
Nutrition labels for foods. Labels providing nutrition facts give consumers information about the nutritional value of food products that they buy. A study of these labels collected data from 152
CHALL ENGE Enjoyment of physical exercise. Although the benefits of physical exercise are well known, most people do not exercise and many who start exercise programs drop out after a short time. A
Demand for non-biotech cereals. A study designed to determine how willing consumers are to pay a premium for non-biotech breakfast cereals (cereals that do not include gene-altered ingredients)
CH ALLENGE More on predicting substance abuse.Refer to the previous exercise. The researchers also studied cigarette use, alcohol use, and cocaine use. Here is a summary of the results for the
Predicting substance abuse. What factors predict substance abuse among high school students? One study designed to answer this question collected data from 89 high school seniors in a suburban
Understanding the tests of significance. Using a new software package, you ran a multiple regression. The output reported an F statistic with P < 0.05, but none of the t tests for the individual
Childhood obsesity. The prevalence of childhood obesity in industrialized nations is constantly rising. Since between 30% and 60% of obese children maintain their obesity into adulthood, there is
More on constructing the ANOVA table. A multiple regression analysis of 73 cases was performed with 5 explanatory variables. Suppose that SSM = 14.1 and SSE = 100.5.(a) Find the value of the F
Constructing the ANOVA table. Seven explanatory variables are used to predict a response variable using a multiple regression.There are 140 observations.(a) Write the statistical model that is the
What’s wrong? In each of the following situations, explain what is wrong and why.(a) One of the assumptions for multiple regression is that the distribution of each explanatory variable is
What’s wrong? In each of the following situations, explain what is wrong and why.(a) In a multiple regression with a sample size of 40 and 4 explanatory variables, the test statistic for the null
More on significance tests for regression coefficients. For each of the settings in the previous exercise, test the null hypotheses that the coefficient of x1 is zero versus the two-sided alternative.
95% confidence intervals for regression coefficients. In each of the following settings, give a 95% confidence interval for the coefficient of x1.(a) n = 30, ˆy = 10.6 + 10.8x1 + 7.9x2, SEb1=
Residual plots for the CSDATA analysis. The CSDATA data set can be found in the Data Appendix. Using a statistical package, fit the linear model with HSM and HSE as predictors and obtain the
Pairwise relationships among variables in the CSDATA data set.The CSDATA data set can be found in the Data Appendix. Using a statistical package, generate the pairwise correlations and scatterplots
ANOVA table for multiple regression. Use the following information to perform the ANOVA F test and compute R2.Degrees Source of freedom Sum of squares Model 175 Error 60 Total 65 1015
Significance tests for regression coefficients. Recall Exercise 11.1(page 610). Due to missing values for some students, only 86 students were used in the multiple regression analysis. The following
Understanding the fitted regression line. The fitted regression equation for a multiple regression isˆy = −1.4 + 2.6x1 − 2.3x2(a) If x1 = 4 and x2 = 2, what is the predicted value of y?(b) For
Describing a multiple regression. As part of a recent study titled“Predicting Success for Actuarial Students in Undergraduate Math graduates were obtained.2 The researchers were interested in
CHALLENGE Inference over different ranges of X.Think about what would happen if you analyzed a subset of a set of data by analyzing only data for a restricted range of values of the explanatory
CHALL ENGE Resting metabolic rate and exercise, continued. Refer to the previous exercise.It is tempting to conclude that there is a strong linear relationship for the women but no relationship for
Resting metabolic rate and exercise. Metabolic rate, the rate at which the body consumes energy, is important in studies of weight gain, dieting, and exercise. The table below gives data on the lean
Personality traits and scores on the GRE.A study reported correlations between several personality traits and scores on the Graduate Record Examination (GRE) for a sample of 342 test takers.22 Here
Food neophobia. Food neophobia is a personality trait associated with avoiding unfamiliar foods.In one study of 564 children who were 2 to 6 years of age, food neophobia and the frequency of
CHALLENGE Index of biotic integrity. Refer to the data on the index of biotic integrity and area in Exercise 10.14 (page 596) and the additional data on percent watershed area that was forest in
CHALLENGE Creating a new explanatory variable.Refer to the previous two exercises.(a) Create a new variable that is the product of length and width. Make a plot and run the regression using this new
C HALLENGE Transforming the perch data. Refer to the previous exercise.(a) Try to find a better model using a transformation of length. One possibility is to use the square. Make a plot and perform
Length, width, and weight of perch. Here are data for 12 perch caught in a lake in Finland:20 Weight Length Width Weight Length Width(grams) (cm) (cm) (grams) (cm) (cm)5.9 8.8 1.4 300.0 28.7 5.1
CHALL ENGE Matching standardized scores. Refer to the previous two exercises. An alternative to the least-squares method is based on matching standardized scores. Specifically, we set( ˆy − y)sy=
CHALL ENGE SAT versus ACT, continued. Refer to the previous exercise. Find the predicted value of ACT for each observation in the data set.(a) What is the mean of these predicted values?Compare it
SAT versus ACT. The SAT and the ACT are the two major standardized tests that colleges use to evaluate candidates. Most students take just one of these tests. However, some students take both.Table
Verifying the effect of bank size. Refer to the bank wages data given in Table 10.8 and described in Exercise 10.37 (page 601). The data also include a variable “Size,” which classifies the bank
Significance test of the correlation. A study reported a correlation r = 0.5 based on a sample size of n = 20; another reported the same correlation based on a sample size of n = 10.For each, perform
Quality of life in chronically ill patients.Concern about the quality of life for chronically ill patients is becoming as important as treating their physical symptoms. The SF-36, a questionnaire for
Standard error and confidence interval for the slope. Refer to the previous two exercises.The standard deviation of the S&P 500 returns for these years is 16.45%. From this and your work in the
Interpreting statistical software output. Refer to the previous exercise. What are the values of the regression standard error s and the squared correlation r2?
Completing an ANOVA table. How are returns on common stocks in overseas markets related to returns in U.S. markets? Measure U.S. returns by the annual rate of return on the Standard &Poor’s 500
Parental behavior and self-esteem. Chinese students from public schools in Hong Kong were the subjects of a study designed to investigate the relationship between various measures of parental
Net flow in stock and bond funds. Is there a nonzero correlation between net flow of money into stock mutual funds and into bond funds? Use the regression analysis you did in Exercise 10.33(page 600)
Capacity of DRAM. The capacity (bits) of the largest DRAM (dynamic random access memory)chips commonly available at retail has increased as follows:17 Year 1971 1980 1987 1993 1999 2000 Bits 1,024
Is this relationship significant? Refer to the previous exercise. Test the null hypothesis that the correlation between the binge-drinking rate and the average price for a bottle of beer within a
Correlation between binge drinking and the average price of beer. A recent study looked at 118 colleges to investigate the association between the binge-drinking rate and the average price for a
Predicting the lean in 2009. Refer to the previous two exercises.(a) How would you code the explanatory variable for the year 2009?(b) The engineers working on the Leaning Tower of Pisa were most
More on the Leaning Tower of Pisa. Refer to the previous exercise.(a) In 1918 the lean was 2.9071 meters. (The coded value is 71.) Using the least-squares equation for the years 1975 to 1987,
Leaning Tower of Pisa. The Leaning Tower of Pisa is an architectural wonder. Engineers concerned about the tower’s stability have done extensive studies of its increasing tilt.Measurements of the
Do wages rise with experience? Refer to the previous exercise. Analyze the data with the outlier included.(a) How does this change the estimates of the parameters β0, β1, and σ?(b) What effect
Do wages rise with experience? We assume that our wages will increase as we gain experience and become more valuable to our employers. Wages also increase because of inflation. By examining a sample
More on MA and HAV. Refer to the previous exercise. Give a 95% confidence interval for the slope. Explain how this interval can tell you what to conclude from a significance test for this parameter.
Severities of MA and HAV. Metatarsus adductus(call it MA) is a turning in of the front part of the foot that is common in adolescents and usually corrects itself. Hallux abducto valgus (call it
Math pretest predicts success? Can a pretest on mathematics skills predict success in a statistics course? The 82 students in an introductory statistics class took a pretest at the beginning of the
Stocks and bonds. How is the flow of investors’money into stock mutual funds related to the flow of money into bond mutual funds? Here are data on the net new money flowing into stock and bond
School budget and number of students.Suppose that there is a linear relationship between the number of students x in an elementary school and the annual budget y. Write a population regression model
CHALL ENGE Neuron responses. Exercise 2.143 (page 163) gives data on neuron responses to pure tones and to monkey calls.(a) Describe each variable graphically and numerically.(b) Plot the data with
Reading test scores and IQ. In Exercise 2.11(page 95) you examined the relationship between a reading test score and an IQ score for a sample of 60 fifth-grade children.(a) Run the regression and
TRAP and bone resorption using logs. Refer to the TRAP and VO– data in Exercise 10.27.Reanalyze these data using the logs of both TRAP and VO–. Summarize your results and compare them with those
Transforming the data. Refer to the OC and VO+data in Exercise 10.26. For variables such as these, it is common to work with the logarithms of the measured values. Reanalyze these data using the logs
CH ALLENGE TRAP and bone resorption. In Exercise 7.119 (page 482) we looked at the distribution of tartrate resistant acid phosphatase (TRAP), a biomarker for bone resorption. Table 10.7 gives values
CHALLENGE Osteocalcin and bone formation. In Exercise 7.118 (page 482) we looked at the distribution of osteocalcin (OC), a biomarker for bone formation, in a sample of 31 healthy females aged 11 to
CRP and serum retinol. In Exercise 7.26 (page 442) we examined the distribution of C-reactive protein (CRP) in a sample of 40 children from Papua New Guinea. Serum retinol values for the same
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