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statistics principles and methods

Questions and Answers of Statistics Principles And Methods

=+and the independent variables x1 5 hydrogen peroxide(% by weight), x2 5 sodium hydroxide (% by weight), x3 5 silicate (% by weight), and x4 5 process temperature(“Advantages of CE-HDP Bleaching
=+14.32 ● This exercise requires the use of a computer package. The accompanying data resulted from a study of the relationship between y 5 brightness of finished paper
=+14.31 This exercise requires the use of a computer package. Use the data given in Exercise 14.27 to verify that the true regression function mean y value 5 a 1 b1x1 1 b2x2 1 b3x3 1 b4x4 1 b5x5 is
=+14.30 Suppose that a multiple regression data set consists of n 5 15 observations. For what values of k, the number of model predictors, would the corresponding model with R2 5 .90 be judged useful
=+the quadratic model specify a useful relationship between y and x? Carry out the appropriate test using a .01 level of significance.
=+the relationship between y 5 yield (kg/plot) and x 5 defoliation level (a proportion between 0 and 1). The estimated regression equation based on n 5 24 was where x1 5 x and x2 5 x 2. The article
=+14.29 The article “Effect of Manual Defoliation on Pole Bean Yield” (Journal of Economic Entomology [1984]:1019–1023) used a quadratic regression model to describe
=+c. Do you think that the estimated regression equation would provide reasonably accurate predictions of error rate? Explain.
=+a. Does the estimated regression equation specify a useful relationship between y and the independent variables? Use the model utility test with a .05 significance level.b. Calculate R 2and se for
=+x3 5 viewing angle, and x4 5 level of ambient light. From a table given in the article, SSRegr 5 19.2, SSResid 5 20.0, and n 5 30.
=+A Response Surface” (Human Factors [1983]: 185–190)used the estimated regression equation to describe the relationship between y 5 error percentage for subjects reading a four-digit liquid
=+c. Use the value of R 2from Part (b) and a .05 level of significance to conduct the appropriate model utility test.14.28 The article “Readability of Liquid Crystal Displays:
=+14.27 ● ▼ The article “The Undrained Strength of Some Thawed Permafrost Soils” (Canadian Geotechnical Journal [1979]: 420–427) contained the accompanying data(see page 658) on y 5 shear
=+c. How does adjusted R 2compare to R 2?
=+b. Given the results of the test in Part (a), does it surprise you that the R 2value is so low? Can you think of a possible explanation for this?
=+a. The reported value of R 2 was .16. Conduct the model utility test. Use a .05 significance level.
=+The estimated regression equation (based on n 5 367 observations) was where x3 5 x1x2.
=+the processing of criminal court cases. Data were collected in the Chicago criminal courts on the following variables:y 5 number of indictments x1 5 number of cases on the docket x2 5 number of
=+14.26 The article “The Caseload Controversy and the Study of Criminal Courts” (Journal of Criminal Law and Criminology [1979]: 89–101) used a multiple regression analysis to help assess the
=+when attempting to determine the quality of fit of the data to our model?c. Perform a model utility test.
=+a. Fit a multiple regression model for predicting the volume (in ml) of a package based on its minimum width, maximum width, and elongation score.b. Why should we consider adjusted R 2instead of R
=+the top of page 658 on dimensions of 27 representative food products.
=+14.25 ● This exercise requires the use of a computer package. The article “Vital Dimensions in Volume Perception: Can the Eye Fool the Stomach?” (Journal of Marketing Research [1999]:
=+e. Which of the two models considered (the multiple regression model from Part (a) or the simple linear regression model from Part (d)) would you recommend for predicting catch time? Justify your
=+d. The authors of the article suggest that a simple linear regression model with the single predictor might be a better model for predicting catch time. Calculate the x values and use them to fit
=+c. Is the multiple regression model useful for predicting catch time? Test the relevant hypotheses using a 5 .05.
=+b. Predict the catch time for an animal of prey whose length is 6 and whose speed is 50.
=+a. Fit a multiple regression model for predicting catch time using prey length and speed as predictors.
=+moved across the screen. The following data are consistent with summary values and a graph given in the article.Each value represents the average catch time over all subjects. The order of the
=+experiment where subjects were asked to “catch” an animal of prey moving across his or her computer screen by clicking on it with the mouse. The investigators varied the length of the prey and
=+Unit Body Length Speed of Prey as an Estimator of Vulnerability to Predation” (Animal Behaviour [1999]: 347–352) found that the speed of a prey (twips/s) and the length of a prey (twips 3 100)
=+14.24 ● This exercise requires the use of a computer package. The authors of the article “Absolute Versus per
=+b. Carry out the model utility test to determine whether the predictors length and age, together, are useful for predicting weight.
=+a. Fit a multiple regression model to describe the relationship between weight and the predictors length and age.
=+14.23 ● This exercise requires the use of a computer package. The article “Movement and Habitat Use by Lake Whitefish During Spawning in a Boreal Lake: Integrating Acoustic Telemetry and
=+14.22 For the multiple regression model in Exercise 14.4, the value of R 2 was .06 and the adjusted R 2 was .06. The model was based on a data set with 1136 observations. Perform a model utility
=+b. Using a .01 significance level, perform the model utility test.c. Interpret the values of R 2and se given in the output.
=+a. What is the estimated regression equation?
=+S = 4.784 R-sq = 90.8% R-sq(adj) = 89.4%Analysis of Variance DF SS MS Regression 4 5896.6 1474.2 Error 26 595.1 22.9 Total 30 6491.7
=+14.21 The accompanying MINITAB output results from fitting the model described in Exercise 14.12 to data.Predictor Coef Stdev t-ratio Constant 86.85 85.39 1.02 X1 –0.12297 0.03276 –3.75 X2
=+14.20 Is the model fit in Exercise 14.15 useful? Carry out a test using a significance level of .10.
=+previous fall academic motivation, x3 5 age, x4 5 number of credit hours, x5 5 residence (1 if on campus, 0 otherwise), x6 5 hours worked on campus, and x7 5 hours worked off campus. The sample
=+14.19 The article “Impacts of On-Campus and Off-Campus Work on First-Year Cognitive Outcomes” (Journal of College Student Development [1994]: 364–370) reported on a study in which y 5 spring
=+shore width, x3 5 drainage (%), x4 5 water color (total color units), x5 5 sand (%), and x6 5 alkalinity. The coefficient of multiple determination was reported as R 2 5 .83.Use a test with
=+Rarities from Habitat Variables: Coastal Plain Plants on Nova Scotian Lakeshores” (Ecology [1992]: 1852–1859)used a sample of n 5 37 lakes to obtain the estimated regression equation where y 5
=+14.18 The ability of ecologists to identify regions of greatest species richness could have an impact on the preservation of genetic diversity, a major objective of the World Conservation Strategy.
=+14.17 Obtain as much information as you can about the P-value for the F test for model utility in each of the following situations:a. k 5 2, n 5 21, calculated F 5 2.47 5 5.98 5 3.00 ed on x1 and
=+14.16 Obtain as much information as you can about the P-value for an upper-tailed F test in each of the following situations:yˆ 5 92 2 2.18x1 2 19.20x2 2 9.38x3 1 2.32x4a. df1 5 3, df2 5 15,
=+. How does it compare to R 2itself?
=+b. What proportion of observed variation in fish intake can be explained by the model relationship?c. Estimate the value of s.d. Calculate adjusted R 2
=+.
=+Part of the data given in the article were used to obtain the estimated regression equation(based on n 5 26). SSRegr 5 1486.9 and SSResid 5 2230.2 were also calculated.a. Interpret the values of b1
=+at Power Station Intakes” (Journal of Applied Ecology[1983]: 33–42) examined intake fish catch at an English power plant and several other variables thought to affect fish intake:
=+14.15 ▼ When coastal power stations take in large quantities of cooling water, it is inevitable that a number of fish are drawn in with the water. Various methods have been designed to screen
=+d. If you were to take logarithms of each side of the equation in Part (a), would the relationship be linear?
=+c. Should we use an additive multiple regression model to predict a volume of a can from its height and width?Explain.
=+b. Is the relationship between volume and its predictors, height and width, a linear one?
=+a. Give the equation that would allow us to make such predictions.
=+14.14 If we knew the width and height of cylindrical tin cans of food, could we predict the volume of these cans with precision and accuracy?
=+b. Suppose that you want to incorporate interaction between age and size class. What additional predictors would be needed to accomplish this?
=+a. Suppose that you want to incorporate size class of car, with four categories (subcompact, compact, midsize, and large), into a regression model that also includes x1 5 age of car and x2 5 engine
=+14.13 ▼ Consider the dependent variable y 5 fuel efficiency of a car (mpg).
=+b. For this particular model, does it make sense to interpret the value of any individual bi(b1, b2, b3, or b4) in the way we have previously suggested? Explain.
=+a. According to this model, what is the mean y value if x1 5 3200 and x2 5 57?
=+(8F). A regression model using and x4 5 x1x2 was suggested:mean y value 5 86.8 2 .123x1 1 5.09x2 2 .0709x3 1 .001x4
=+14.12 The article “The Value and the Limitations of High-Speed Turbo-Exhausters for the Removal of Tar-Fog from Carburetted Water-Gas” (Society of Chemical Industry Journal [1946]: 166–168)
=+d. The model that includes as predictors all independent variables, all quadratic terms, and all interaction terms(the full quadratic model)
=+c. All models that include as predictors all independent variables, no quadratic terms, and exactly one interaction term
=+x2 5 planting density 1plants/ha2 x1 5 planting date 1days after April 202 y 5 percent maize yieldb. The model that includes as predictors all independent variables and all quadratic terms
=+a. The model that includes as predictors all independent variables but no quadratic or interaction terms y 5 1.8 1 .1x1 1 .8x2 1 e x4 5 x 22 2x3 5 x 21
=+14.11 Consider a regression analysis with three independent variables x1, x2, and x3. Give the equation for the following regression models:
=+b. What additional predictors would be needed to incorporate interaction between temperature and intake setting?
=+a. Write a model equation that includes dummy variables to incorporate intake setting, and interpret all the b coefficients.
=+14.10 A manufacturer of wood stoves collected data on y 5 particulate matter concentration and x1 5 flue temperature for three different air intake settings (low, medium, and high).
=+How do they differ from those obtained in Parts (a) and (b)?
=+d. Suppose the interaction term .03x3 where x3 5 x1x2 is added to the regression model equation. Using this new model, construct the graphs described in Parts (a) and (b).
=+c. What aspect of the graphs in Parts (a) and (b) can be attributed to the lack of an interaction between x1 and x2?
=+b. Construct a graph depicting the relationship between mean y and x1 for fixed values 50, 55, and 60 of x2.
=+a. Construct a graph (similar to that of Figure 14.5) showing the relationship between mean y and x2 for fixed values 10, 20, and 30 of x1.
=+14.9 Suppose that the variables y, x1, and x2 are related by the regression model
=+d. Is it legitimate to interpret b1 5 .653 as the true average change in yield when planting date increases by one day and the values of the other three predictors are held fixed? Why or why not?
=+c. Would the mean yield be higher for a planting date of May 6 or May 22 (for the same density)?
=+b. Use the regression function in Part (a) to determine the mean yield for a plot planted on May 6 with a density of 41,180 plants/ha.
=+a. If a 5 21.09, b1 5 .653, b2 5 .0022, b3 5 2.0206, and b4 5 .00004, what is the population regression function?
=+b1x1 1 b2x2 1 b3x3 1 b4x4 1 e where and provides a good description of the relationship between y and the independent variables.
=+14.8 The relationship between yield of maize, date of planting, and planting density was investigated in the article “Development of a Model for Use in Maize Replant Decisions” (Agronomy
=+c. What is the change in mean chlorine content when the degree of delignification increases from 8 to 9? From 9 to 10?
=+b. Would mean chlorine content be higher for a degree of delignification value of 8 or 10?
=+x values between 2 and 12. (Substitute x 5 2, 4, 6, 8, 10, and 12 to find points on the graph, and connect them with a smooth curve.)
=+a. Graph the regression function 220 1 75x 2 4x 2over
=+ ess Reversion: Influence of ess Reversion of Bleached I [1964]: 653–662) pro-odel to describe the rela-delignification during the processing of wood pulp for paper and y 5 total chlorine
=+b. What mean error percentage is associated with a backlight level of 20, character subtense of .5, viewing angle of 10, and ambient light level of 30?c. Interpret the values of b2 and b3.
=+a. Assume that this is the correct equation. What is the mean value of y when x1 5 10, x2 5 .5, x3 5 50, and x4 5 100?
=+y 5 error percentage for subjects reading a four-digit liquid crystal display x1 5 level of backlight (from 0 to 122 cd/m)x2 5 character subtense (from .025° to 1.34°)x3 5 viewing angle (from 0°
=+14.6 The article “Readability of Liquid Crystal Displays:A Response Surface” (Human Factors [1983]: 185–190)used a multiple regression model with four independent variables, where
=+c. Interpret the values of the population regression coefficients.
=+b. What is the mean yield when the mean temperature and percentage of sunshine are 18.9 and 43, respectively?
=+a. Suppose that this equation does indeed describe the true relationship. What mean yield corresponds to a temperature of 20 and a sunshine percentage of 40?y 5 415.11 2 6060x1 2 4.50x2 1 e 2
=+14.5 ▼ The article “The Influence of Temperature and Sunshine on the Alpha-Acid Contents of Hops” (Agricultural Meteorology [1974]: 375–382) used a multiple regression model to relate y 5
=+d. How would you interpret the coefficient of x2?e. Comment on the numerical coding of the ideology and social class variables. Can you suggest a better way of incorporating these two variables

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