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Statistics The Exploration And Analysis Of Data 6th Edition John M Scheb, Jay Devore, Roxy Peck - Solutions

=+b. Which transformation considered in Part (a) does the best job of producing an approximately linear relationship? Use the selected transformation to predict lead content when distance is 25 m.
=+5.72 ● The article “Reduction in Soluble Protein and Chlorophyll Contents in a Few Plants as Indicators of Automobile Exhaust Pollution” (International Journal of Environmental Studies [1983]: 239–244) reported the following data on x 5 distance from a highway (in meters)and y 5 lead
=+e. Using just the results of Parts (a) and (c), what is the value of Pearson’s sample correlation coefficient?
=+d. Calculate and interpret the value of se.
=+c. What percentage of observed variation in y can be explained by the approximate linear relationship between the two variables?
=+b. Calculate SSResid and SSTo.
=+5.71 ● The following data on the relationship between degree of exposure to 242Cm alpha radiation particles (x)and the percentage of exposed cells without aberrations(y) appeared in the paper “Chromosome Aberrations Induced in Human Lymphocytes by DT Neutrons” (Radiation Research [1984]:
=+c. Does the least-squares line appear to give accurate predictions? Explain your reasoning.
=+in which x values were for anterior teeth. Consider the following representative subset of the data:x 15 19 31 39 41 y 23 52 65 55 32 x 44 47 48 55 65 y 60 78 59 61 60 a 5 32.080888 b 5 0.554929a. Calculate the predicted values and residuals.b. Use the results of Part (a) to obtain SSResid and r
=+2 and se.5.70 ● The paper cited in Exercise 5.69 gave a scatterplot
=+5.69 The paper “Root Dentine Transparency: Age Determination of Human Teeth Using Computerized Densitometric Analysis” (American Journal of Physical Anthropology [1991]: 25–30) reported on an investigation of methods for age determination based on tooth characteristics. With y 5 age (in
=+c. What happens if the line in Part (a) is used to predict the myoglobin level for a finishing time of 8 hr? Is this reasonable? Explain.
=+a. Obtain the equation of the least-squares line.b. Interpret the value of b.
=+5.68 ● Athletes competing in a triathlon participated in a study described in the paper “Myoglobinemia and Endurance Exercise” (American Journal of Sports Medicine[1984]: 113–118). The following data on finishing time x(in hours) and myoglobin level y (in nanograms per milliliter) were
=+b. Predict lichen dry weight percentage for an NO3 deposition of 0.5 g/m3.
=+a. What is the equation of the least-squares regression line?
=+5.67 ● The article “The Epiphytic Lichen Hypogymnia physodes as a Bioindicator of Atmospheric Nitrogen and Sulphur Deposition in Norway” (Environmental Monitoring and Assessment [1993]: 27–47) gives the following data(read from a graph in the paper) on x 5 NO3 wet deposition(in grams per
=+b. Construct a scatterplot. From the plot, does the word linear really provide the most effective description of the relationship between x and y? Explain.
=+5.66 ● The accompanying data represent x 5 the amount of catalyst added to accelerate a chemical reaction and y 5 the resulting reaction time:x 1 2 3 4 5 y 49 46 41 34 25a. Calculate r. Does the value of r suggest a strong linear relationship?
=+5. In the context of this activity, write a brief description of the danger of extrapolation.
=+4. If there appears to be a relationship between age and flexibility, fit a model that is appropriate for describing the relationship.
=+3. After your class has collected appropriate data, use them to construct a scatterplot. Comment on the interesting features of the plot. Does it look like there is a relationship between age and flexibility?
=+2. Working as a class, decide on a reasonable way to collect data on the two variables of interest.
=+1. Age and the measure of flexibility just described will be measured for a group of individuals. Our goal is to determine whether there is a relationship between age and this measure of flexibility. What are two reasons why it would not be a good idea to use just the students in your class as
=+Materials needed: Yardsticks.In this activity you will investigate the relationship between age and a measure of flexibility. Flexibility will be measured by asking a person to bend at the waist as far as possible, extending his or her arms toward the floor.Using a yardstick, measure the distance
=+3. Using your mouse, you can move the line and see how the deviations from the line and the sum of squared errors change as the line changes. Try to move the line into a position that you think is close to the least-squares regression line. When you think you are close to the line that minimizes
=+The black points in the plot represent the data set, and the blue line represents a possible line that might be used to describe the relationship between the two variables shown. The pink lines in the graph represent the deviations of points from the line, and the pink bar on the lefthand side
=+Now open the applet called RegDecomp. You should see a screen that looks like the one shown here:Copyright 2008 Thomson Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.
=+2. Reset the plot (by clicking on the Reset bar in the lower left corner of the screen) and add points trying to produce a data set with a correlation that is close to 1.4. Briefly describe the factors that influenced where you placed the points.
=+1. Using the mouse, you can click to add points to form a scatterplot. The value of the correlation coefficient for the data in the plot at any given time (once you have two or more points in the plot) will be displayed at the top of the screen. Try to add points to obtain a correlation
=+Open the applet (available in ThomsonNOW at www.thomsonedu.com/login) called CorrelationPoints.You should see a screen like the one shown below.
=+d. In order to avoid a “wardrobe malfunction,” one would like to use fabric that has less than a 5% chance of failing.Suppose that this fabric is our choice for a new shirt. To have less than a 5% chance of failing, what would you estimate to be the maximum “safe” load in lb/sq in.?
=+c. What proportion of the time would you estimate this fabric would fail if a load of 60 lb/sq in. were applied?
=+b. Using the techniques introduced in this section, calculate for each of the loads and fit the line(Load). What is the significance of a positive slope for this line?
=+a. Make a scatterplot of the proportion failing versus the load on the fabric.
=+5.65 ● In the study of textiles and fabrics, the strength of a fabric is a very important consideration. Suppose that a significant number of swatches of a certain fabric are subjected to different “loads” or forces applied to the fabric.The data from such an experiment might look as
=+c. The point at which the dose kills 50% of the pests is sometimes called LD50, for “Lethal dose 50%.” What would you estimate to be LD50 for this pesticide and for mosquitoes?
=+b. Using the techniques introduced in this section, calculate for each of the concentrations and fit the line (Concentration). What is the significance of a positive slope for this line?
=+a. Make a scatterplot of the proportions of mosquitoes killed versus the pesticide concentration.
=+5.64 ● The hypothetical data below are from a toxicity study designed to measure the effectiveness of different doses of a pesticide on mosquitoes. The table below summarizes the concentration of the pesticide, the sample sizes, and the number of critters dispatched.Concentration (g/cc) 0.10
=+c. Using the best-fit line from Part (b), estimate the proportion of plots of land on which Lobaria oregano are classified as “common” at an elevation of 900 m.
=+b. Using the techniques introduced in this section, calculate for each of the elevations and fit the line (Elevation). What is the equation of the best-fit line?
=+a. As elevation increases, does Lobaria oregano become more common or less common? What aspect(s) of the table support your answer?
=+Elevation (m) 400 600 800 1000 1200 1400 1600 Prop. of plots with Lichen(.10/plot) 0.99 0.96 0.75 0.29 0.077 0.035 0.01
=+5.63 ● As part of a study of the effects of timber management strategies (Ecological Applications [2003]1110–1123) investigators used satellite imagery to study abundance of the lichen Lobaria oregano at different elevations. Abundance of a species was classified as “common” if there
=+d. At what point in time does the estimated proportion of hatching for cloud forest conditions seem to cross from greater than 0.5 to less than 0.5?
=+c. Using your best-fit line from Part (b), what would you estimate the proportion of eggs that would, on average, hatch if they were exposed to cloud forest conditions for 3 days? 5 days?
=+b. Using the techniques introduced in this section, calculate for each of the exposure times in the cloud forest and fit the line (Days). What is the significance of a negative slope to this line?
=+a. Plot the data for the low- and mid-elevation experimental treatments versus exposure. Are the plots generally the shape you would expect from “logistic” plots?
=+5.62 ● The paper “The Shelf Life of Bird Eggs: Testing Egg Viability Using a Tropical Climate Gradient” (Ecology [2005]: 2164–2175) investigated the effect of altitude and length of exposure on the hatch rate of thrasher eggs.Data consistent with the estimated probabilities of hatching
=+5.61 ● Anabolic steroid abuse has been increasing despite increased press reports of adverse medical and psychiatric consequences. In a recent study, medical researchers studied the potential for addiction to testosterone in hamsters(Neuroscience [2004]: 971–981). Hamsters were allowed to
=+Construct a scatterplot for this data set. Would you describe the relationship between age and canal length as linear? If not, suggest a transformation that might straighten the plot.
=+ data set that appeared in the paper “Validation of Age Estimation in the Harp Seal Using Dentinal Annuli” (Canadian Journal of Fisheries and Aquatic Science [1983]: 1430–1441):x 0.25 0.25 0.50 0.50 0.50 0.75 0.75 1.00 y 700 675 525 500 400 350 300 300 x 1.00 1.00 1.00 1.00 1.25 1.25 1.50
=+. Is this effective in straightening the plot? Explain.5.60 ● Determining the age of an animal can sometimes be a difficult task. One method of estimating the age of h l i b d th idth f the pulp canal in the the relationship between al, researchers measured own age. The following 5 canal
=+d. Now consider a scatterplot that uses transformations on both x and y: log(y) and x 2
=+c. Draw a scatterplot that uses log(y) and x. The log(y)values, given in order corresponding to the y values, are 0.95, 0.85, 0.78, 1.70, 0.70, 2.00, 0.85, 1.15, 1.15, 1.00, 1.70, 1.15, 1.70, 2.18, 1.00, 1.83, 2.00, and 2.00. How does this scatterplot compare with that of Part (b)?
=+. Does this transformation straighten the plot?
=+b. The scatterplot in Part (a) is curved upward like segment 2 in Figure 5.31, suggesting a transformation that is up the ladder for x or down the ladder for y. Try a scatterplot that uses y and x 2
=+a. Construct a scatterplot of y versus x. Is the scatterplot compatible with the statement of positive association made in the paper?
=+x 1.0 26.0 1.1 101.0 14.9 134.7 y 9 7 6 50 5 100 x 3.0 5.7 7.6 25.0 143.0 27.5 y 7 14 14 10 50 14 x 103.0 180.0 49.6 140.6 140.0 233.0 y 50 150 10 67 100 100
=+5.59 ● The paper “Population Pressure and Agricultural Intensity” (Annals of the Association of American Geographers [1977]: 384–396) reported a positive association between population density and agricultural intensity. The following data consist of measures of population density(x) and
=+a. x and yc. x andb. and yd. ande. x and log(y) (values of log(y) are 0.26, 0, 20.30, 21, and 21)
=+5.58 ● Penicillin was administered orally to five different horses, and the concentration of penicillin in the blood was determined after five different lengths of time. The following data appeared in the paper “Absorption and Distribution Patterns of Oral Phenoxymethyl Penicillin in the
=+e. What would you predict success to be when the energy of shock is 1.75 times the threshold level? When it is 0.8 times the threshold level?
=+c. Consider transforming the data by leaving y unchanged and using either or . Which of these transformations would you recommend? Justify your choice by appealing to appropriate graphical displays.
=+b. Fit a least-squares line to the given data, and construct a residual plot. Does the residual plot support your conclusion in Part (a)? Explain.
=+5.57 ● A study, described in the paper “Prediction of Defibrillation Success from a Single Defibrillation Threshold Measurement” (Circulation [1988]: 1144–1149) investigated the relationship between defibrillation success and the energy of the defibrillation shock (expressed as a
=+d. The prediction made in Part (c) involves prediction for an x value that is outside the range of the x values in the sample. What assumption must you be willing to make for this to be reasonable? Do you think this assumption is reasonable in this case? Would your answer be the same if the
=+c. Using the transformed variables from Part (b), fit a least-squares line and use it to predict the number waiting for an organ transplant in 2000 (Year 11).
=+b. The scatterplot in Part (a) is shaped like segment 2 in Figure 5.31. Find a transformation of x and/or y that straightens the plot. Construct a scatterplot for your transformed variables.
=+a. Construct a scatterplot of the data with y 5 number waiting for transplant and x 5 year. Describe how the number of people waiting for transplants has changed over time from 1990 to 1999.
=+year from 1990 to 1999. The following data are approximate values and were read from the graph in the article:Number Waiting for Transplant Year (in thousands)1 (1990) 22 2 25 3 29 4 33 5 38 6 44 7 50 8 57 9 64 10 (1999) 72
=+5.56 ● The article “Organ Transplant Demand Rises Five Times as Fast as Existing Supply” (San Luis Obispo Tribune, February 23, 2001) included a graph that showed the number of people waiting for organ transplants each 1x 1y 1y 1x
=+b. Because the scatterplot of the original data appeared curved, transforming both the x and y values by taking square roots was suggested. Calculate the correlation coefficient for the variables and . How does this value compare with that calculated in Part (a)? Does this indicate that the
=+a. Calculate the correlation coefficient for these data.
=+b. One possible transformation that might lead to a straighter plot involves taking the square root of both the x and y values. Use Figure 5.31 to explain why this might be a reasonable transformationc. C.Partd. U migh 5.55 Data on salmon availability (x) and the percentage of eagles in the air
=+a. Draw a scatterplot for this data set. Would you describe the plot as linear or curved?
=+5.54 ● The paper “Aspects of Food Finding by Wintering Bald Eagles” (The Auk [1983]: 477–484) examined the relationship between the time that eagles spend aerially searching for food (indicated by the percentage of eagles soaring) and relative food availability. The accompanying data were
=+e. Using the transformed variables, fit the least-squares line and use it to predict the fatality rate for 78-year-old drivers.
=+d. Does the scatterplot in Part (c) suggest that the transformation was successful in straightening the plot?
=+c. Reexpress x and/or y using the transformation you recommended in Part (b). Construct a scatterplot of the transformed data.
=+b. Using Table 5.5 and the ladder of transformations in Figure 5.31, suggest a transformation that might result in variables for which the scatterplot would exhibit a pattern that was more nearly linear.
=+5.53 ● ▼ The report “Older Driver Involvement in Injury Crashes in Texas” (Texas Transportation Institute, 2004)included a scatterplot of y 5 fatality rate (percentage of ersus x 5 driver age. The ate values read from the Fatality Age Rate Age Rate 40 0.75 80 2.20 45 0.75 85 3.00 50 0.95
=+e. Do you think that predictions of moisture content using the model in Part (c) will be better than those using the model fit in Example 5.16, which used transformed y values but did not transform x? Explain.
=+d. Use the MINITAB output to predict moisture content when frying time is 35 sec.
=+c. Based on the accompanying MINITAB output, does the least-squares line effectively summarize the relationship between y9 and x9?The regression equation is log(moisture) = 2.02 – 1.05 log(time)Predictor Coef SE Coef T P Constant 2.01780 0.09584 21.05 0.000 log(time) –1.05171 0.07091 –14.83
=+a. Construct a scatterplot of the data. Would a straight line provide an effective summary of the relationship?b. Here are the values of x9 5 log(x) and y9 5 log(y):x9 y9 Constr comm
=+5.52 ● The following data on x 5 frying time (in seconds) and y 5 moisture content (%) appeared in the paper“Thermal and Physical Properties of Tortilla Chips as a Function of Frying Time” (Journal of Food Processing and Preservation [1995]: 175–189):x 5 10 15 20 25 30 45 60 y 16.3 9.7
=+d. Referring to Part (c), suppose that you wanted to predict the past value of 6-year-old height from knowledge of 18-year-old height. Find the equation for the appropriate least-squares line. What is the corresponding value of se?
=+2.5 in.What would se be for the least-squares line used to predict 18-year-old height from 6-year-old height?
=+At age 6, average height < 46 in., standard deviation
=+c. A study by the Berkeley Institute of Human Development (see the book Statistics by Freedman et al., listed in the back of the book) reported the following summary data for a sample of n 5 66 California boys:r < .80
=+b. For what values of r will se be much smaller than sy?
=+a. For what value of r is se as large as sy? What is the least-squares line in this case?
=+5.51 Some straightforward but slightly tedious algebra shows that from which it follows that Unless n is quite small, (n 2 1)/(n 2 2) < 1, so
=+c. Explain why it is desirable to have r 2large and se small if the relationship between two variables x and y is to be described using a straight line.
=+2 and se that are both small? Explain. (Again, a picture might be helpful.)
=+2 and se could be large for a bivariate data set? Explain. (A picture might be helpful.)b. Is it possible that a bivariate data set could yield values of r
=+2 and se are used to assess the fit of a line.a. Is it possible that both r
=+b. What is the value of the sample correlation coefficient?yˆ 5 62.9476 2 0.54975x a 5 5.20683380 b 5 20.3421541 a x 5 1060 a y 5 15.8 a xy 5 1601.1c. Suppose that SSTo 5 2520.0 (this value was not given in the paper). What is the value of se?5.50 Both r

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