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applied statistics and multivariate

Questions and Answers of Applied Statistics And Multivariate

(Problem 12.22continued) Based on your results, what is the estimated probability of reporting emotional injuries for a 30-year-old white female renter? For a 50-year-old Latino home owner?
(Problem 12.22 continued) Fit a logistic regression model using emotional injury (yes/no, W238) as an outcome and using home ownership status (rent/own, V449), age (RAGE), gender(RSEX), and ethnicity
This problem and the following ones use the Northridge earthquake data set. We wish to answer the questions: Were homeowners more likely than renters to report emotional injuries as a result of the
For the model in 12.20 use the referent time as given by the variable HMONTH to define the offset. Run the same model as in 12.20. Present rate ratios, including confidence intervals, and interpret
For the Parental HIV data perform a Poisson regression on the number of days the adolescents were absent from school without a reason. For this analysis assume that the referent time period was one
For the model in 12.18 find an appropriate cutoff point to discriminate between adolescents who were absent without a reason and those who were not. Assess how well the model predicts the outcome
Perform a binary logistic regression analysis using the Parental HIV data to model the probability of having been absent from school without a reason (variable HOOKEY). Find the variables that best
Perform a nominal and ordinal logistic regression analysis using the health scale as the outcome variable and age and income as independent variables. Present and interpret the results for an
For the family lung function data perform a nominal logistic regression where the outcome variable is place of residence and the predictors are those defined in Problem 12.11. Test the hypothesis
For the depression data perform an ordinal logistic regression analysis using the same outcome categories as in Section 12.9 which reverses the order and hence compares more severe depression to less
Generate a graph for income similar to Figure 12.2 to assess whether modeling income linearly seems appropriate.
Perform a logistic regression analysis for the depression data which includes income and sex and models age as ana) quadratic orb) cubic function. Use likelihood ratio test statistics to determine
Assume a logistic regression model includes a continuous variable like age and a categorical variable like gender and an interaction term for these. Is the P value for any of the main effects helpful
For the family lung function data set, define a new variable VALLEY (residence in San Gabriel or San Fernando Valley) to be one if the family lives in Burbank or Glendora and zero otherwise.Using
Using the definition of low FEV1 given in Problem 12.9, perform a logistic regression of low FEV1 on area for the fathers. Include all four areas and use a dummy variable for each area.What is the
Define low FEV1 to be an FEV1 measurement below the median FEV1 of the fathers in the family lung function data set given in Appendix A. What are the odds that a father in this data set has low FEV1?
Repeat Problem 12.7, but for chronic rather than acute illness.
Using the depression data set, appropriate variable selection techniques, and logistic regression, describe the probability of an acute illness as a function of age, education, income, depression,
(a) Using the depression data set, fill in the following table:What are the odds that a woman is a regular drinker? That a man is a regular drinker? What is the odds ratio?(b) Repeat the tabulation
Perform a logistic regression analysis on the data described in Problem 11.2.
Perform a logistic regression analysis with the same variables and data used in the example in Problem 11.13.
The accompanying table presents the number of individuals by smoking and disease status.What are the odds that a smoker will get disease A? That a nonsmoker will get disease A?What is the odds ratio?
Using the formula odds = P=(1????P), fill in the accompanying table. Odds P 0.25 0.20 0.5 1.0 0.5 1.5 2.0 2.5 3.0 0.75 5.0
If the probability of an individual getting a hit in baseball is 0.20, then the odds of getting a hit are 0.25. Check to determine that the previous statement is true. Would you prefer to be told
Calculate the Parental Bonding Overprotection and Parental Bonding Care score for the Parental HIV data (see Appendix A and the codebook). Perform a discriminant function analysis to classify
Refer to the table of ideal weights given in Problem 10.8 and calculate the midpoint of each weight range for men and women. Pretending these represent a real sample, perform a discriminant function
Is it possible to distinguish between men and women in the depression data set on the basis of income and level of depression? What is the classification function? What are your prior probabilities?
Divide the oldest children in the family lung function data set into two groups based on weight:less than or equal to 101 versus greater than 101. Perform a stepwise discriminant function analysis
(a) In the family lung function data in Appendix A divide the fathers into two groups: group I with FEV1 less than or equal to 4.09, and group II with FEV1 greater than 4.09. Assuming equal prior
At the time the study was conducted, the population of Lancaster was 48,027 while Glendora had 38,654 residents. Using prior probabilities based on these population figures and those given in Problem
From the family lung function data in Appendix A create a data set containing only those families from Burbank and Long Beach (AREA = 1 or 3). The observations now belong to one of two AREA-defined
(Continuation of Problem 11.7.) Do a variable selection analysis, using variables X4 to X9 only. Comment.
(Continuation of Problem 11.7.) Do a variable selection analysis for all nine variables. Comment.
(Continuation of Problem 11.7.) Perform a similar analysis, using only X1, X2, and X3. Test the hypothesis that these three variables do as well as all nine classifying the observations.Comment.
(Y is not used here). Then for the first 50 cases, add 6 to X1, add 3 to X2, add 5 to X3, and leave the values for X4 to X9 as they are. For the last 50 cases, leave all the data as they are. Thus
In this problem you will modify the data set created in Problem 8.7 to make it suitable for the theoretical exercises in discriminant analysis. Generate the sample data for X1, X2,. . . ,X9 as in
(Continuation of Problem 11.2.) Now divide the companies into three groups: group I consists of those companies with a P/E of 7 or less, group II consists of those companies with a P/E of 8 to 10,
(Continuation of Problem 11.2.) Perform a variable selection analysis, using stepwise and best-subset programs. Compare the results with those of the variable selection analysis given in Chapter 9.
(Continuation of Problem 11.2.) Choose a different set of prior probabilities and costs of misclassification that seems reasonable and repeat the analysis.
(Continuation of Problem 11.2.) Test whether D/E alone does as good a classification job as all six variables.
For the data shown in Table 9.1, divide the chemical companies into two groups: group I consists of those companies with a P/E less than 9, and group II consists of those companies with a P/E greater
Using the depression data set, perform a stepwise discriminant function analysis with age, sex, log(income), bed days, and health as possible variables. Compare the results with those given in
For the variables describing the average number of cigarettes smoked during the past 3 months(SMOKEP3M) and the variable describing the mother’s education (EDUMO) in the Parental HIV data determine
Using the data from the Parents HIV/AIDS study, for those adolescents who have started to use alcohol, predict the age when they first start their use (AGEALC). Predictive variables should include
Using dummy variables, run a regression analysis that relates CESD as the dependent variable to marital status in the depression data set given in Chapter 3. Do it separately for males and females.
Using the family lung function data, find the regression of height for the oldest child on mother’s and father’s height. Include a dummy variable for the sex of the child and any necessary
Perform a ridge regression analysis of the family lung function data using FEV1 of the oldest child as the dependent variable and height, weight and age of the oldest child as the independent
Using the family lung function data, relate FEV1 to height for the oldest child in three ways:simple linear regression (Problem 7.9), regression of FEV1 on height squared, and spline regression
In the depression data set, define Y = the square root of total depression score (CESD), X1 =log(income), X2 = Age, X3 = Health and X4 = Bed days. Set X1 = missing whenever X3 = 4(poor health). Also
Take the family lung function data described in Appendix A and delete (label as missing) the height of the middle child for every family with ID divisible by 6, that is, families 6, 12, 18 etc.(To
(Continuation of Problem 10.8.) Using the data in the table given in Problem 10.8, compute the midpoints of weight range for all frame sizes for men and women separately. Pretending that the results
Use the data described in Problem 8.7. Since some of the X variables are intercorrelated, it may be useful to do a ridge regression analysis of Y on X1 to X9. Perform such an analysis, and compare
Unlike the real data used in Problem 10.5, the accompanying data are “ideal” weights published by the Metropolitan Life Insurance Company for American men and women. Compute Y = midpoint of
(Continuation of Problem 10.5.) Do a similar analysis for the first boy and girl. Include age and age squared in the regression equation.
Another way to answer the question of interaction between the independent variables in Problem 8.13 is to define a dummy variable that indicates whether an observation is above the median weight, and
Use the lung function data described in Appendix A. For the parents we wish to relate Y =weight to X = height for both men and women in a single equation. Using dummy variables, write an equation for
Draw a ridge trace for the accompanying data. Variable Case X1 X2 X3 Y 12345678 0.46 0.96 6.42 3.46 0.06 0.53 5.53 2.25 1.49 1.87 8.37 5.69 1.02 0.27 5.37 2.36 1.39 0.04 5.44 2.65 0.91 0.37 6.28 3.31
In the depression data set, determine whether religion has an effect on income when used as an independent variable along with age, sex, and educational level.
Repeat Problem 10.1, but now use a dummy variable for education. Divide the education level into three categories: did not complete high school, completed at least high school, and completed at least
In the depression data set described in Chapter 3, data on educational level, age, sex, and income are presented for a sample of adults from Los Angeles County. Fit a regression plane with income as
Using the Parental HIV data find the best model that predicts the age at which adolescents started drinking alcohol among those who have started drinking alcohol. Since the data were collected
Using the Parental HIV data consider performing a confirmatory data analysis investigating the relationship between the age at which children started drinking alcohol (if they have already started)
From among the candidate variables given in Problem 9.11, find the subset of three variables that best predicts height in the oldest child, separately for boys and girls. Are the two sets the same?
Using the methods described in this chapter and the family lung function data described in Appendix A, and choosing from among the variables OCAGE, OCWEIGHT, MHEIGHT, MWEIGHT, FHEIGHT, and FWEIGHT,
Force the variables you selected in Problem 9.9(a) into the regression equation with OCFEV1 as the dependent variable, and test whether including the FEV1 of the parents (i.e., the variables MFEV1
(a) For the lung function data set described in Appendix A with age, height, weight, and FVC as the candidate independent variables, use subset regression to find which variables best predict FEV1 in
In Problem 8.7 the population multiple R2 of Y on X4, X5,. . . , X9 is zero. However, from the sample alone we don’t know this result. Perform a variable selection analysis on X4 to X9, using your
For the data from Problem 8.7, perform a variable selection analysis, using the methods described in this chapter. Comment on the results in view of the population parameters.
Use the data you generated from Problem 8.7, where X1, X2,. . . ,X9 are the independent variables and Y is the dependent variable. Use the generalized linear hypothesis test to test the hypothesis
Using the data given in Table 9.1, repeat the analyses described in this chapter with (P/E)1=2 as the dependent variable instead of P/E. Do the results change much? Does it make sense to use the
For adult males it has been demonstrated that age and height are useful in predicting FEV1.Using the data described in Appendix A, determine whether the regression plane can be improved by also
includes data for both years(Forbes, vol. 127, no. 1 (January 5, 1981) and Forbes, vol. 131, no. 1 (January 3, 1983)). Do a forward stepwise regression analysis, using P/E as the dependent variable
Forbes gives, each year, the same variables listed in Table 9.1 for the chemical industry. The changes in lines of business and company mergers resulted in a somewhat different list of chemical
Repeat Problem 9.1 using subset regression, and compare the results.
Use the depression data set described in Table 3.4. Using CESD as the dependent variable, and age, income, and level of education as the independent variables, run a forward stepwise regression
For the Parental HIV data generate a variable that represents the sum of the variables describing the neighborhood where the adolescent lives (NGHB1–NGHB11). Is the age at which adolescents start
Repeat Problem 8.15(a) for fathers’ measurements instead of those of the oldest children. Are the regression coefficients more stable? Why?
(Continuation of Problem 8.13.)a) For the oldest child, find the regression of FEV1 on (i) weight and age; (ii) height and age; (iii)height, weight, and age. Compare the three regression equations.
(Continuation of Problem 8.13.) Find the partial correlation of FEV1 and age given height for the oldest child, and compare it to the simple correlation between FEV1 and age of the oldest child. Is
For the lung function data described in Appendix A, find the regression of FEV1 on weight and height for the fathers. Divide each of the two explanatory variables into two intervals:greater than, and
(Continuation of Problem 8.11.) For the regression of CESD on INCOME and AGE, choose 15 observations that appear to be influential or outlying. State your criteria, delete these points, and repeat
(Continuation of Problem 8.5.) Fit a regression plane for CESD on INCOME and AGE for males and females combined. Test whether the regression plane is helpful in predicting the values of CESD. Find a
(Continuation of Problem 8.7.) Perform a multiple regression analysis, with the dependent variable = Y and the independent variables = X1 to X9, on the 100 generated cases. Summarize the results and
(Continuation of Problem 8.7.) Calculate the population partial correlation coefficient between X2 and X3 after removing the linear effect of X1. Is it larger or smaller than r23? Explain. Also,
Repeat Problem 8.7 using another statistical package and see if you get the same sample.
Using a statistical package of your choice, create a hypothetical data set which you will use for exercises in this chapter and some of the following chapters. Begin by generating 100 independent
Search for a suitable transformation for CESD if the normality assumption in Problem 8.5 cannot be made. State why you are not able to find an ideal transformation if that is the case.
From the depression data set described in Table 3.4, predict the reported level of depression as given by CESD, using INCOME, SEX, and AGE as independent variables. Analyze the residuals and decide
Fit the regression plane for mothers with MFVC as the dependent variable and age and height as the independent variables. Summarize the results in a tabular form. Test whether the regression results
Write the results for Problem 8.2 so they would be suitable for inclusion in a report. Include table(s) that present the results the reader should see.
Fit the regression plane for the fathers using FFVC as the dependent variable and age and height as the independent variables.
Using the chemical companies’ data in Table 9.1, predict the price earnings (P/E) ratio from the debt to equity (D/E) ratio, the annual dividends divided by the 12-months’ earnings per share
Using the summary variable describing the neighborhood in Problem 7.15, generate a loess graph to examine the relationship between this variable and the age at which adolescents started using
For the Parental HIV data generate a variable that represents the sum of the variables describing the neighborhood where the adolescent lives (NGHB1–NGHB11). Does the age at which adolescents start
For the Parental HIV data produce a scatterplot of the age at which adolescents first started smoking versus the age at which they first started drinking alcohol. Based on the graph, do adolescents
For the mother, perform a regression of FEV1 on weight. Test whether the coefficients are zero. Plot the regression line on a scatter diagram of MFEV1 versus MWE1. On this plot, identify the
Examine the residual plot from the regression of FEV1 on height for the oldest child. Choose an appropriate transformation, perform the regression with the transformed variable, and compare the
What is the correlation between height and weight in the oldest child? How would your answer to the last part of Problem 7.10 change if r = 1? r = ????1? r = 0?
For the oldest child, perform the following regression analyses: FEV1 on weight, FEV1 on height, FVC on weight, and FVC on height. Note the values of the slope and correlation coefficient for each
From the depression data set described in Table 3.4 create a data set containing only the variables AGE and INCOME.a) Find the regression of income on age.b) Successively add and then delete each of

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