Modern Applied Statistics With S-PLUS 3rd Edition W. N. Venables, B. D. Ripley - Solutions

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1. Workouts are necessary to keep you healthy. Although we all know the importance of keeping an active lifestyle, school and work demands usually get in the way. Here is a list of 20 college students’ number of workouts during last week.
6. The normal distribution curve is symmetric around which point of the distribution?1. mean 2. median 3. mode 4. all of the above
5. In a negatively skewed distribution, the mean would be 1. larger than the median.2. smaller than the median.
2. it is not affected much by extreme values of the variable. It remains relatively stable even with extreme values in the variable.
1. its calculation does not involve every value in the variable, and
4. A __________ skewed distribution is a distribution with a high concentration of data points at the low end of the values and a long tail toward the high end of the values.1. positively 2. negatively 3. doubly 4. exponentially
3. Which one of the following variables is most likely to be used to create histograms?1. Nominal variables 2. Ordinal variables 3. Discrete variables 4. Continuous variables?
2. When constructing a frequency table with equal intervals of a continuous variable X, each interval consists of same width. To make sure that there is no overlap between two adjacent intervals, each interval actually includes 1. lower limit < X < upper limit.2. lower limit ≤ X < upper limit.3.
1. In a statistics class, students’ quiz scores on a pop quiz with only four questions were reported in the frequency table below. Use the frequency table to calculate the total quiz score for the class.
4. Make sure that there is no overlap between two adjacent intervals. For continuous variables, each interval includes the lower limit but not the upper limit.
3. Create the equal intervals in an ascending order.
2. Choose an appropriate and convenient interval, usually in 5s or 10s if feasible, to construct a frequency table with 7 ± 2 equal intervals.
1. Identify the minimal and maximal values of the variable. Calculate the range.
Adjust the mean formula when using frequency tables?
Calculate mean from the formula
Differentiate among the three common central tendency measures: (1) mode, (2) median, and (3) mean
Define the positively skewed and negatively skewed distributions
Identify the common distribution shapes
Identify the differences between bar graphs and histograms
Create a frequency distribution table with equal intervals to summarize data
Construct a frequency distribution table with individual values to summarize data
13. X = 4, 5, 6, and 9; Y = −1, −1, 1, and 2; compute (∑XY)2 and∑(X − 5)(Y + 1)
12. X = 3, 4, 5, and 7; Y = −1, 0, 1, and 2; compute ∑X 2Y 2 and∑(X − 2)(Y − 3)
11. X = 3, 4, 5, and 7; Y = −1, 0, 1, and 2; compute ∑XY and(∑XY)2
10. X = −3, 0, 1, and 2; compute ∑X, ∑(X − 1)2, and ∑X 2 − 3
9. X = 3, 4, 5, and 7; compute ∑X, (∑X)2, and ∑X 2
8. The measure of income is an example of a(n) __________ scale of measurement.1. nominal 2. ordinal 3. interval 4. ratio
7. Which of the following pairs is usually unknown parameters of the population?1. and µ2. s and σ3. s 2 and σ2 4. µ and σ
6. The measure of temperature in Fahrenheit is an example of a(n)__________ scale of measurement.1. nominal 2. ordinal 3. interval 4. ratio
5. Gender, religion, and ethnicity are measurements on a(n)__________ scale.1. nominal 2. ordinal 3. interval 4. ratio
4. For X = 0, 1, 6, 3, what is (∑X)2?1. 20 2. 46 3. 64 4. 100
3. What additional characteristic is required on a ratio scale compared with an interval scale?1. Whether the measurements are the same or different 2. The order of the magnitudes 3. An absolute zero 4. Scores with equal units
2. A quantity, usually an unknown numerical value that describes a population, is a __________.1. parameter 2. statistic 3. population 4. sample
1. A researcher was interested in the sleeping habits of college students. A group of 50 students were selected at random and interviewed. The researcher found that these students slept an average of 6.7 hours per day. For this study, the 50 students are an example of a __________.1. parameter 2.
3. Where X = 1, 2, 3, and 4, and Y = 2, 4, 6, and 8, compute ∑(X −3)(Y − 5) and ∑X 2Y 2.
2. Researchers investigated the gender gap in pay for physicians.An online salary survey was sent out to the members of the American Medical Association with an electronic link. What type of research was this study? What kind of sample was likely to be obtained by this online survey?
1. Researchers studied the effect of driving while texting on driving mistakes. College students were recruited to participate in the study. Due to risk of actual driving on the road, researchers conducted the research in a lab with a driving simulator. Students were randomly assigned to one of the
7. What type of research design is used in this study?
6. What is the dependent variable of this study?
5. What is the independent variable of this study?
How can we assess the strength of the conclusions?
How can we analyze the data and draw conclusions?
How should we organize the data?
How many data are needed to provide sufficient guidance?
What kind of data need to be collected?
Identify numeric characteristics of each scale of measurement?
Provide two or three examples of each scale of measurement
Define scales of measurement
Define descriptive statistics and inferential statistics
Define samples and populations
9.1. This data frame gilgais was collected on a line transect survey in gilgai territory in New South Wales, Australia. Gilgais are natural gentle depressions in otherwise flat land, and sometimes seem to be regularly distributed. The data collection was stimulated by the question: are these
9.2. Exercise 6.5 considered linear regression for the GAG in urine data in data frame GAGurine. Consider using a non-linear or smooth regression for the same task.
9.3. Use neural networks to fit a smooth curve to the mcycle data used in Figure 9.1. Investigate ways of choosing the degree of smoothness automatieally.
11.1. Data frame biopsy contains data on 699 biopsies of breast tumours, which have been elassified as benign or malignant (Mangasarian & Wolberg, 1990). The nine variables on each biopsy are a rating (1 to 10) by the coordinating physician; ratings on one variable are missing for some biopsies.
11.2. Data frame UScereals describes 65 commonly available breakfast cereals in the USA, based on the information available on the mandatory food label on the packet. The measurements are normalized to a serving size of one American cup.(i) Is there any way to discriminate among the major
13.1. Our dataset accdeaths gives monthly accidental deaths in the USA 1973-8, from Brockwell & Davis (1991). Find a suitable ARIMA model, and predict the deaths for the first six months of 1979.
13.2. Dataset austres is a quarterly series of the number of Australian residents from March 1971 to March 1994. It comes from Brockwell & Davis(1996) who analyse the percentage quarterly changes. Explore suitable models in S-PLUS.
13.3. Repeat Exercise 9.1 as a time series problem.
13.4. Use the information gained in the analysis of beavl in Section 13.5 to refine the analysis for beav2.
13.5. Consider the problem of estimating the effect of seat belt legislation on road accident casualties in the UK considered by Harvey & Durbin (1986). The data (from Harvey, 1989) are in the series drivers.
2.1. How would you find the index(es) of specified values within a vector? For example, where is the hill race (in hills) with a climb of 2100 feet?
2.2. The column ftv in data frame birthwt counts the number of visits.Reduce this to a factor with levels 0, 1 and '2 or more'. [Hint: manipulate the levels, or investigate functions cut and merge . levels.]
2.3. Write a simple function to compute the median absolute deviation (used in robust statistics; see Section 5.5) medianix - /-LI with default /-L the sampie median. Compare YOUf answer with the S-PLUS function mad.
2.4. Suppose x is an object with named components and out is a character string vector. How would you make a new object obtained from x by excluding any components whose names are in out?
2.5. Given a matrix X of distinct rows and a vector W of the number of times that each row should occur, reconstruct the original matrix.
2.6. "I calculated a cross-correlation matrix. 1 want to print only members of this matrix that are larger than 0.90 and 1 want to include dimnames in the answer."
2.7. "I have a large data frame (5000 observations) and 1 would like the cases where a variable indicating ethnic group is in (1,3,4,6,7)."
3.1. The data frame survey contains the results of a survey of 237 first-year statistics students at Adelaide University. For a graphical summary of all the variables, use plot (survey). Note that this produces a dotchart for factor variables, and a normal scores plot for the numeric variables.One
3.2. Make a plot of petal width versus petallength of the iris data for a partially sighted audience, identifying the three species. You will need to double the annotation size, thicken the lines and change the layout to allow larger margins for the larger annotation.
3.3. Plot sin(x) against x, using 200 values of x between -'Ir and 'Ir, but do not plot any axes yet (use parameter axes=F in the call to plot). Add a y-axis passing through the origin using the 'extended' style and horizontal labels. Add an x-axis with tick-marks from -'Ir to 'Ir in increments of
3.4. Cleveland (1993) recommends that the aspect ratio of line plots is chosen so that lines are 'banked' at 450
By this he means that the averaged absolute value of the slope should be around ±45°. Write a function to achieve this for a time-series plot, and try it out on the sunspots dataset. (Average along the arc length of the curve. See the function banking for Cleveland's solution.)
3.5. The Trellis function splom produces a complete matrix of scatterplots, as does the basic plotting functions pairs, but in earlier versions of S-PLUS pairs only plotted the lower triangle of the matrix. Write a function to emulate the earlier behaviour. [Hint: look at pairs. def ault. The
3.6. Ternary plots are used for compositional data (Aitchison, 1986) where there are three components whose proportions add to one. These are represented by a point in an equilateral triangle, where the distances to the sides add to a constant.Write an S function to plot a matrix of compositions on
5.1. Rice (1995, p. 390) gives the following data (Natrella, 1963) on the latent heat of the fusion of ice (cal/gm):Method A: 79.98 80.04 80.02 80.04 80.03 80.03 80.04 79.97 80.05 80.03 80.02 80.00 80.02 Method B: 80.02 79.94 79.98 79.97 79.97 80.03 79.95 79.97(a) Assuming normality, test the
5.2. Write functions to produce Q-Q plots for a gamma and a Weibull distribution. Note that unlike the normal Q-Q plot, the shape parameters may need to be estimated.
5.3. The ideas used in bandwidth selection for kernel density estimation that are implemented in width. SJ can also be applied to the choice of bin width in a histogram (Wand, 1997). Implement such a bin-width estimator in S.
5.4. Experiment with dataset galaxies. How many modes do you think there are in the underlying density?
6.1. Apply regression diagnostics to the fits to the whi teside energy consumption data. Note (Figure 6.1) that the evidence for a quadratic fit to the 'after'data sterns from points with high leverage, so also try resistant fits.
6.2. Dataset cabbages gives the results of a field trial on the growth of cabbages (Rawlings, 1988, p. 219). Analyse this trial.
6.3. The data frame rubber in the library MASS gives 30 measurements of rubber loss under accelerated testing together with the hardness and tensile strength of the rubber itself. Explore the data in brush, then fit linear and quadratic regressions of 10ss on hard and tens. Select a suitable
6.4. Criminologists are interested in the effect of punishment regimes on crime rates. This has been studied using aggregate data on 47 states of the USA for 1960, available in data frame UScrime (Ehrlich, 1973; Vandaele, 1978; Raftery, 1995). The response variable is the rate of crimes in a
6.5. Susan Prosser collected data on the concentration of a chemical GAG in the urine of 314 children aged from 0 to 17 years. The data are in data frame GAGurine. Analyse these data, and produce achart to help a paediatrican to assess if a child's GAG concentration is 'normal'.
6.6. The Janka hardness data in data frame janka gives the density (Dens)and hardness (Hard) of a sampie of Australian Eucalypt hardwoods. The problem is to build aprediction equation for hardness in terms of density.
6.7. The Cars93 data frame (Lock, 1993) gives data on 93 new car models on sale in the USA in 1993. Use this dataset to predict fuel consumption from the remaining variables. [Hint: The fuel consumption is in miles per US gallon. In metric units fue1 consumption is expressed in litres/lOOkm, a
6.8. The data in Table 6.4 (from Scheffe, 1959, and in data frame genotype)refer to rat litters the at were separated from their natural mothers at birth and given to foster mothers to rear. The rats were classified into one of four genotypes, A, B, land J. The response is the litter average weight
6.9. Extend the analysis of the coop dataset to an the specimens.
6.10. Add the fitted lines for the final model for the petrol data to Figure 6.9.
6.11. Find a way to plot the Si tka data that facilitates comparison of the growth curves for the two treatment groups.Add to your plot the fitted mean growth curve and some 95% confidence intervals.
6.12. Consider how to explore the assumptions made for the lme model for the Si tka data. Are the plot methods for lme objects helpful in this?
6.13. The object Sitka89 contains the 1989 data on the same 79 Sitka trees measured on eight days in 1989. Analyse the 1989 data separately, and then in conjunction with the 1988 data.
7.1. Explore the anorexia data example introduced in the discussion of offsets on page 217 and report your final linear model.Begin with a Trellis display of the data showing post-treatment weight against pre-treatment weight for the three treatment groups. In each panel inelude the individual
7.2. Analyse the menarche dataset on the proportions of female children in Warsaw at various ages during adolescence who have reached menarche (Milicer& Szczotka, 1966) using both logit and probit links.
7.3. Knight & Skagen (1988) collected the data shown in the table (and in data frame eagles) during a field study on the foraging behaviour of wintering Bald Eagles in Washington State, USA. The data concern 160 attempts by one(pirating) Bald Eagle to steal a chum salmon from another (feeding) Bald
7.4. The following data are part of a survey by Dr Mutch of low-weight births in Scotland between 1981 and 1988. The table refers to 661 children with birth weights between 650g and 1749g all of whom survived for at least one year. The variables of interest are:
7.5. A survey was made of bicycle and other traffic in the neighbourhood of the Berkeley campus of the University of Califomia in 1993 (Gelman et al., 1995, p. 91). Sixty city streets were selected at random, with a stratification into three levels of activity and whether the street had a marked
7.6. To study the relative survival capacities of two species of native and exotic snails, here labelIed A and B, groups of 20 animals were held in controlled laboratory conditions for periods of 1, 2, 3 or 4 weeks. At the end of the period the animals were checked for whether they had survived,
7.7. An experiment was performed in Sweden in 1961-2 to assess the effect of speed limits on the motorway accident rate (Svensson, 1981). The experiment was conducted on 92 days in each year, matched so that day j in 1962 was comparable to day j in 1961. On some days the speed limit was in effect
7.8. The data given in data frame Insurance consist of the numbers of policyholders n of an insurance company who were exposed to risk, and the numbers of car insurance claims made by those policyholders in the third quarter of 1973(Baxter, Coutts & Ross, 1980, Aitkin et al., 1989. The data are
8.1. For the weight loss example compare the negative exponential model with quadratic and cubic polynornial regression alternative models, in particular check the behaviour of each model under extrapolation into the future.

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Modern Applied Statistics With S-PLUS 3rd Edition W. N. Venables, B. D. Ripley - Solutions

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