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legal research analysis

Questions and Answers of Legal Research Analysis

Table 6.5, available in the Alligators2 data file at the text website, displays primary food choice for a sample of alligators, classified by length (≤2.3 meters,>2.3 meters) and by the lake in
For the alligator food choice example (Section 6.1.2), use the model fit to estimate an odds ratio that describes the effect of length on primary food choice being either invertebrate or other.
A model fit predicting preference for President in the US (Democrat, Republican, Independent) using x = annual income (in $10,000 dollars) is log(ˆπD/πˆI )=3.3 −0.2x and log(ˆπR/πˆI
The following are true–false questions.a. A model for a binary y has a continuous explanatory variable. If the model truly holds, the residual deviance has a distribution approaching chi-squared as
The width values in the Crabs data file have a mean of 26.3 and standard deviation of 2.1. If the true relationship is the fitted equation reported in Section 4.1.3, logit[π(x)] = −12.351 +
We expect success probabilities for two groups to be about 0.20 and 0.30, and we want an 80% chance of detecting a difference using a 90% confidence interval.a. Assuming equal sample sizes, how large
For the Crabs data file, fit the linear probability model to the probability that a female horseshoe crab with shell width x has a satellite. Is the fit adequate for large x values?
Refer to the SoreThroat data file introduced in Exercise 4.16. Fit and interpret the main effects (a) linear probability model, (b) probit model.
Refer to Exercise 4.1 on cancer remission. Table 5.10 shows output for fitting a probit model. Interpret the parameter estimates (a) finding the remission value at which the estimated probability of
Table 5.9 shows results of a randomized clinical trial conducted at five centers. The purpose was to compare an active drug to placebo for treating fungal infections (1 =success, 0 = failure). For
Table 5.8 is from a study of nonmetastatic osteosarcoma described in the LogXact 7 manual (Cytel Software, 2005, p. 171). The response is whether the subject achieved a three-year disease-free
Refer to Exercise 5.4. With veg as the response variable, find a logistic model for which at least one ML effect estimate is infinite. Explain the aspect of the data file that causes this. Report and
Suppose y = 0 at x = 0, 10, 20, 30 and y = 1 at x = 70, 80, 90, 100.a. Explain intuitively why βˆ = ∞ for the model, logit[P(Y = 1)] = α + βx. Reportβˆ and its SE for the software you use.b.
Refer to the model you selected in part (a) of Exercise 5.4. Check goodness of fit.Can you conduct a residual analysis with this data file? Explain.
The Lungs data file at the text website13 summarizes eight studies in China about smoking and lung cancer. Analyze these data and prepare a short report that summarizes your analyses and
Table 5.7 shows a 2 × 2 × 6 contingency table for y = whether admitted to graduate school at the University of California, Berkeley, for fall 1973, by gender of applicant for the six largest
Refer to Table 2.9 on death penalty decisions. Fit a logistic model with the two race predictors. Conduct a residual analysis and interpret.
For data introduced in Exercise 4.10 about AIDS symptoms, AZT use, and race, here is some R output:-------------------------------------–-------------------------------------> fit
Refer to the previous exercise. The data file also shows responses on whether a person smokes frequently. Software reports model −2 log-likelihood values of 1130.23 with only an intercept term,
Exercise 4.12 introduced four scales of the Myers–Briggs personality test.Table 5.6 shows SAS output for fitting a model using the four scales as predictors of whether a subject drinks alcohol
The Students data file at the text website shows responses of a class of social science graduate students at the University of Florida to a questionnaire that asked about gender (1 = female, 0 =
The Crabs2 data file at the text website shows several variables that may be associated with y = whether a female horseshoe crab is monandrous (eggs fertilized by a single male crab) or polyandrous
Table 7.8 in Chapter 7 shows data from the Substance2 data file at the text website. Create a new data file from which you can build a logistic regression model for these data, treating marijuana use
For the horseshoe crabs data file, fit a model using weight and width as explanatory variables for the probability of a satellite.a. Conduct a likelihood-ratio test of H0: β1 = β2 = 0. Interpret.b.
The PSA blood test is designed to detect prostate cancer. Suppose that of men who have this disease, the test fails to detect prostate cancer in 1 in 4, and of men who do not have it, 1 in 10 have
For diagnostic testing, let X = true status (1 = disease, 2 = no disease) and Y = diagnosis (1 = positive, 2 = negative). Let π1 = P(Y = 1 | X = 1) andπ2 = P(Y = 1 | X = 2). Let γ denote the
According to recent UN figures, the annual gun homicide rate is 62.4 per one million residents in the US and 1.3 per one million residents in Britain. Compare the proportion of residents killed
The opening 2018 World Cup odds against being the winning team specified by espn.com were 9/2 for Germany, 5/1 for Brazil, 11/2 for France, 20/1 for England, and 7/1 for Spain. Find the corresponding
Consider the following two studies reported in the New York Times:a. A British study reported that of smokers who get lung cancer, “women were 1.7 times more vulnerable than men to get small-cell
Finding and interpreting measures comparing proportions:a. An observational study19 of patients hospitalized for gunshot wounds in the US between 2004 and 2013 classified the intent of the gunshot
For adults who sailed on the Titanic on its fateful voyage, the odds ratio20 between gender (female, male) and survival (yes, no) was 11.4.a. What is wrong with the interpretation, “The probability
A research study estimated that under a certain condition, the probability a subject would be referred for heart catheterization was 0.906 for whites and 0.847 for blacks.a. A press release about the
A 20-year study of British male physicians22 noted that the proportion who died from lung cancer was 0.00140 per year for cigarette smokers and 0.00010 per year for nonsmokers. The proportion who
Table 2.10 shows fatality results for drivers and passengers in auto accidents in Florida in 2015, according to whether the person was wearing a shoulder and lap belt restraint versus not using one.
Table 2.11 cross-classifies votes in the 2008 and 2012 US Presidential elections. Estimate and find a 95% confidence interval for the population odds ratio. Interpret.
Data posted at the FBI website (www.fbi.gov) indicated that of all blacks slain in 2015, 92% were slain by blacks, and of all whites slain in 2015, 93% were slain by whites. Let Y denote race of
Refer to Table 2.1 about belief in an afterlife. Conduct a test of statistical independence. Report the P-value and interpret.
A poll by Louis Harris and Associates of 1249 adult Americans indicated that 36%believe in ghosts and 37% believe in astrology. Can you compare the proportions using inferential methods for
An article23 summarized results from the Nurses’ Health Study and the Health Professionals Follow-Up Study. The article reported (with RR = relative risk) that “Compared with nonregular use,
Table 2.12 shows data from a General Social Survey cross-classifying a person’s perceived happiness with their family income. The table displays the observed and expected cell counts and the
Table 2.13 is based on data from the 2016 General Social Survey.a. Test the null hypothesis of independence between political party identification and race. Interpret.b. Use standardized residuals to
Each subject in a sample of 100 men and 100 women is asked to indicate which of the following factors (one or more) are responsible for increases in teenage crime:A – the increasing gap in income
Table 2.14 is from a recent General Social Survey. For these data, X2 = 69.2. Write a short report summarizing inference. In your report, mention an alternative test of independence that is relevant
Formula (2.3) has alternative formula X2 = n(ˆπij − πˆi+πˆ+j )2/πˆi+πˆ+j . Explain why, for particular {πˆij}, X2 is large when n is sufficiently large, regardless of whether the
A GSS that cross-classified income in thousands of dollars (25) by job satisfaction (very dissatisfied, a little satisfied, moderately satisfied, very satisfied) for black Americans produced a 4 × 4
A study (B. Kristensen et al., J. Intern. Med. 232: 237–245 (1992)) considered the effect of prednisolone on severe hypercalcaemia in women with metastatic breast cancer. Of 30 patients, 15 were
Table 2.15 contains results of a study comparing radiation therapy with surgery in treating cancer of the larynx. Some R output
a. At each age level, the death rate is higher in South Carolina than in Maine, but overall the death rate is higher in Maine.24 Explain how this could be possible.b. Smith and Jones are baseball
In murder trials in 20 Florida counties during 1976 and 1977, the death penalty was given in 19 out of 151 cases in which a white killed a white, in 0 out of 9 cases in which a white killed a black,
Give an example of three variables X, Y , and Z, for which you expect X and Y to be marginally associated but conditionally independent, controlling for Z.
Based on murder rates in the United States, the Associated Press reported that the probability a newborn child has of eventually being a murder victim is 0.0263 for nonwhite males, 0.0049 for white
The expected frequencies in Table 2.16 show a hypothetical relationship among three variables: Y = response, X = drug treatment, and Z = clinic. Show that X and Table 2.16 Expected frequencies
Refer to Table 2.1 about belief in an afterlife.a. Treating the data as independent binomial samples and using beta(0.5, 0.5) prior distributions, find the posterior mean estimates for the
True or false?a. A 95% confidence interval for the odds ratio between MI (yes, no) and treatment(placebo, aspirin) is (1.44, 2.33). If we form the table with aspirin in the first row(instead of
Describe the purpose of the link function of a GLM. Define the identity link and explain why it is not often used with a binomial parameter.
In the years 1904, 1914, 1924, ... , 2014, the percentage of times the starting pitcher pitched a complete game were7: 87.6, 55.0, 48.7, 43.4, 45.2, 34.0, 24.5, 28.0, 15.0, 8.0, 3.1, 2.4.a. The
For Table 2.6 on x = mother’s alcohol consumption and Y = whether a baby has sex organ malformation, ML fitting of the linear probability model with x scores 0, 0.5, 1.5, 4.0, 7.0 has
In the 2000 U.S. Presidential election, Palm Beach County in Florida was the focus of unusual voting patterns apparently caused by a confusing “butterfly ballot.” Many voters claimed they voted
Access the horseshoe crab data file (shown partly in Table 3.2) at www.stat.ufl.edu/~aa/cat/data. In the data file, y = 1 if a crab has at least one satellite and y = 0 otherwise.a. Using weight as
From the 2016 General Social Survey, when we cross-classify political ideology(with 1 being most liberal and 7 being most conservative) by political party affiliation for subjects of ages 18–27, we
Fit the logistic regression model of Section 3.2.3 to Table 3.1 on snoring and heart disease. Show results of significance tests and confidence intervals for the effect of snoring.
Table 3.4, the Credit data file at the text website, shows data for a sample of 100 adults randomly selected for an Italian study on the relation between x = annual income and y = whether you have a
A recent General Social Survey asked “How many people at your work place are close friends?” The 756 responses had a mean of 2.76, standard deviation of 3.65, and a mode of 0. Would the Poisson
An experiment analyzes imperfection rates for two processes used to fabricate silicon wafers for computer chips. For treatment A applied to 10 wafers, the numbers of imperfections are 8, 7, 6, 6, 3,
Refer to the previous exercise.a. Test H0: μA = μB by conducting the Wald or likelihood-ratio test of H0: β = 0.Interpret.b. Construct a 95% confidence interval for μB/μA. (Hint: Construct one
For the Crabs data file (partially shown in Table 3.2) at www.stat.ufl.edu/~aa/cat/data, fit the Poisson loglinear model to use weight to predict the number of satellites.a. Report the prediction
If you are modeling count data, explain why it is not sufficient to analyze ordinary raw residuals, (yi − μˆi), as you would for ordinary linear models.
True or false?a. An ordinary regression model that treats Y as normally distributed is a special case of a GLM, with a normal random component and identity link function.b. With a GLM, Y does not
A study8 investigated characteristics associated with y = whether a cancer patient achieved remission (1 = yes, 0 = no). An important explanatory variable was a labeling index (LI = percentage of
Refer to the previous exercise. Using information from Table 4.5:a. Conduct a Wald test for the LI effect and construct a 95% Wald confidence interval for the odds ratio corresponding to a 1-unit
Refer to the previous two exercises. Set up the data file as 14 observations in groupeddata format. Compare to the Remissions data file at the text website. Fit the model with this data file. Are the
For the snoring and heart disease data of Table 3.1 (Section 3.2.3) with snoring-level scores (0, 2, 4, 5), the logistic regression ML fit is logit[Pˆ(Y = 1)] = −3.866 +0.397x. Interpret the
For the 23 space shuttle flights before the Challenger mission disaster in 1986, Table 4.6 and the Shuttle data file at the text website shows the temperature (◦F)at the time of the flight and
For Exercise 3.9 on travel credit cards, use the logistic output there to (a) interpret the effect of income on the odds of possessing a travel credit card, and conduct (b) a significance test and
Hastie and Tibshirani (1990, p. 282) described a study to determine risk factors for kyphosis, which is severe forward flexion of the spine following corrective spinal surgery. The Kyphosis data file
For the Crabs data file at the text website, fit the logistic regression model for the probability of a satellite (y = 1) using x = weight as the sole explanatory variable.a. Report the ML prediction
For the Crabs data file, fit a logistic regression model for the probability of a satellite, using color alone as the predictor.a. Treat color as a nominal-scale factor. Report the prediction
In a study9 on the effects of AZT in slowing the development of AIDS symptoms, 338 veterans whose immune systems were beginning to falter after infection with the AIDS virus were randomly assigned
For Table 2.9 on racial characteristics and the death penalty, create a data file and fit a logistic model for death penalty as the response, with defendant’s race and victims’race as
At the website www.stat.ufl.edu/~aa/intro-cda/data for the 2nd edition of this book, the MBTI data file cross-classifies a sample of people from the MBTI Step II National Sample on whether they
For first-degree murder convictions10 in East Baton Rouge Parish, Louisiana, between 1990 and 2008, the death penalty was given in 3 out of 25 cases in which a white killed a white, in 0 out of 3
Table 4.8 shows results of an eight-center clinical trial to compare a drug to placebo for curing an infection. At each center, subjects were randomly assigned to treatments.Analyze these data,
In a study designed to evaluate whether an educational program makes sexually active adolescents more likely to obtain condoms, adolescents were randomly assigned to two experimental groups. The
Table 4.10, which is the SoreThroat data file at the text website, shows results of a study about y = whether a patient having surgery with general anesthesia experienced a sore throat on waking (1 =
Table 4.11 shows estimated effects for a logistic regression model for y = presence of squamous cell esophageal cancer (1 = yes, 0 = no). Smoking status (s) equals 1 for at least one pack per day and
on effects on esophageal cancer.Variable Effect P-value Intercept −7.00
For Table 4.12 from the 2016 General Social Survey, create a data file and analyze the data using logistic regression. Summarize your analyses in a short report, including edited output in an
For model (4.3) for the horseshoe crabs with color and width predictors, add three terms to permit interaction between color and width.a. Report the prediction equations relating width to the
Refer to Exercise 4.12 about MBTI and alcohol drinking.a. When the sample proportion of 0.092 who reported drinking alcohol frequently is the cutpoint for forming a classification table, sensitivity
Explain how the classification table in Table 4.4 with π0 = 0.50 was constructed.Estimate the sensitivity and specificity, and interpret.
You plan to study the relation between x = age and y = whether a member of Facebook (1 = yes, 0 = no). A priori, you predict that P(Y = 1) is currently about 0.80 at x = 18 and about 0.20 at x = 65.
Table 7.8 in Chapter 7 shows data from the Substance2 data file at the text website.Create a new data file from which you can use logistic regression to analyze these data, treating marijuana use as
Refer to the following artificial data:----------------–----------------------------------------------------x number of trials number of successes 04 1 14 2 24
1. Compute all mixed second-order partial derivatives of each of the following functions and verify that the mixed partial derivatives are equal.(a) f(x,y) = xeY • (b) f(x, y) = cos(xy).x+y(c) f
2. Compute all first-order partial derivatives of each of the following functions and find where they are continuous.(a) f(x,y) = x2 +sin(xy). (b) f(x,y,z) =~. (c) f(x,y) = Jx2 +y2.l+z
3. For each of the following functions, compute f x, and determine where it is continuous.(a)(b)(x, y) =I (0,0)(x, y) = (0,0).(x, y) =I (0,0)(x,y) = (0,0).
4. Suppose that H = [a, b] x [c, d] is a rectangle, f : H ~ R is continuous, and 9 : [a, bj ~ R is integrable. Prove that F(y) = lb g(x)f(x, y) dx is uniformly continuous on [c, dj.
5. Evaluate each of the following expressions.(a) lim *cos(xy + xy) dr.
6. Suppose that f is a continuous real function.(a) If f01 f(x) dx = 1, prove that 12 2 2 lim f(lx-1I)e x y+y dx=2.Y-->O 0(b) If f is C1 on Rand f; f'(x) sin x dx =e, prove that e + lim r f(x) cos(y5
*7. Evaluate each of the following expressions.(a) lim r1 xcosy dx.y-->O+ 10 -ij1 - x + y(b) -d dx 100 e-XY sin x dy 11" X at y = 1.

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