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statistics principles and methods

Questions and Answers of Statistics Principles And Methods

=+St. resid. 21.55 0.68 1.25 20.05 21.06 Construct a standardized residual plot. What does the plot suggest about the adequacy of the simple linear regression model?
=+b. The estimated regression line for these data is 5 127 2 6.65x and the standardized residuals are as given.x 0 2 4 6 8
=+a. Construct a scatterplot for these data. Does the plot suggest that the simple linear regression model might be appropriate?
=+13.30 ● The article “Effects of Gamma Radiation on Juvenile and Mature Cuttings of Quaking Aspen” (Forest Science [1967]: 240–245) reported the following data on x 5 exposure to radiation
=+d. Is there anything about the standardized residual plot that would cause you to question the use of the simple linear regression model to describe the relationship between x and y?
=+c. Construct a standardized residual plot. Are there any unusually large residuals?
=+b. Construct a normal probability plot of the standardized residuals. Does the assumption that the random deviation distribution is normal appear to be reasonable? Explain.
=+a. What assumptions are required for the simple linear regression model to be appropriate?
=+standardized residuals.x 4 5 6 9 14 y 0.75 1.20 0.55 0.60 0.65 St. resid. 20.28 1.92 20.90 20.28 0.54 x 15 15 19 21 22 y 0.55 0.00 0.35 0.45 0.40 St. resid. 0.24 22.05 20.12 0.60 0.52
=+13.29 ● ▼ The authors of the article “Age, Spacing and Growth Rate of Tamarix as an Indication of Lake Boundary Fluctuations at Sebkhet Kelbia, Tunisia” (Journal of Arid Environments
=+d. Do you think that the assumptions of the simple linear regression model are reasonable? Give statistical evidence for your answer.
=+c. Interpret the estimated slope and, if appropriate, the intercept.
=+b. Calculate the standardized residuals (or just the residuals if you don’t have access to a computer program that gives standardized residuals), and plot them to determine whether there are any
=+a. Fit the simple linear regression model that would allow prediction of the maximum width (in cm) of a food container based on its minimum width (in cm).
=+Maximum Minimum Product Width Width 11 2.90 2.80 12 2.45 2.10 13 2.60 2.20 14 2.60 2.60 15 2.70 2.60 16 3.10 2.90 17 5.10 5.10 18 10.20 10.20 19 3.50 3.50 20 2.70 1.20 21 3.00 1.70 22 2.70 1.75 23
=+13.28 ● The article “Vital Dimensions in Volume Perception: Can the Eye Fool the Stomach?” (Journal of Marketing Research [1999]: 313–326) gave the accompanying data on the dimensions of
=+13.2 time to exhaustion and y 5 20-km ski time. The x values and corresponding standardized residuals from a simple linear regression are as follows.x 7.7 8.4 8.7 9.0 9.6 9.6 St. resid. 0.10 1.13
=+Do these new experimental data strongly contradict prior belief?
=+n 5 7 Homo erectus fossils.x (chord length in mm) 78 75 78 81 84 86 87 y (capacity in cm3) 850 775 750 975 915 1015 1030 Suppose that from previous evidence, anthropologists had believed that for
=+13.26 ● In anthropological studies, an important characteristic of fossils is cranial capacity. Frequently skulls are at least partially decomposed, so it is necessary to use other
=+Do these data strongly suggest that there is a negative linear relationship between temperature and pH? State and test the relevant hypotheses using a significance level of .01.
=+13.25 ● ▼ The article “Effect of Temperature on the pH of Skim Milk” (Journal of Dairy Research [1988]: 277–280) reported on a study involving x 5 temperature (8C)under specified
=+b. Use a 90% confidence interval to estimate the average change in growth rate associated with a 1-unit increase in expenditure. Interpret the resulting interval.
=+a. Would a simple linear regression model provide useful information for predicting growth rate from research and development expenditure? Use a .05 level of significance.
=+13.24 ● The article “Technology, Productivity, and Industry Structure” (Technological Forecasting and Social Change [1983]: 1–13) included the accompanying data on x 5 research and
=+a significance level of .05. What does your conclusion say about the nature of the relationship between x and y?b. Consider the hypothesis H0: b 5 40 versus Ha: b . 40.The null hypothesis states
=+13.23 Exercise 13.16 described a regression analysis in which y 5 sales revenue and x 5 advertising expenditure.Summary quantities given there yield n 5 15 b 5 52.27 sb 5 8.05a. Test the hypothesis
=+Estimate the mean change in the sunburn index associated with an increase of 1 cm in distance in a way that includes information about the precision of estimation.
=+13.22 ● The article “Effects of Enhanced UV-B Radiation on Ribulose-1,5-Biphosphate, Carboxylase in Pea and Soybean” (Environmental and Experimental Botany [1984]:131–143) included the
=+: a 5 0 cannot be rejected at the .05 significance level, suggesting that a model with a y intercept of 0 might be an appropriate model. Fitting such a model results in an estimated regression
=+c. It is also possible to test hypotheses about the y intercept in a linear regression model. For these data, the null hypothesis H0
=+b. Do the sample data support the hypothesis that there is a useful linear relationship between the mean response time for individuals with no head injury and the mean response time for
=+a. Fit a linear regression model that would allow you to predict the mean response time for those suffering a closed-head injury from the mean response time on the same task for individuals with no
=+Mean Response Time Study Control CHI 1 250 303 2 360 491 3 475 659 4 525 683 5 610 922 6 740 1044 Mean Response Time Study Control CHI 7 880 1421 8 920 1329 9 1010 1481 10 1200 1815
=+13.21 ● The accompanying data were read from a plot(and are a subset of the complete data set) given in the article “Cognitive Slowing in Closed-Head Injury” (Brain and Cognition [1996]:
=+s = 14.30 R-sq = 28.6% R-sq(adj) = 19.7%Analysis of Variance Source DF SS MS F p Regression 1 654.8 654.8 3.20 0.111 Error 8 1635.7 204.5 Total 9 2290.5
=+data are for anterior teeth.x 15 19 31 39 41 44 47 48 55 65 y 23 52 65 55 32 60 78 59 61 60 Use the accompanying MINITAB output to decide whether the simple linear regression model is useful.The
=+13.20 ● The article “Root Dentine Transparency: Age Determination of Human Teeth Using Computerized Densitometric Analysis” (American Journal of Physical Anthropology [1991]: 25–30)
=+b. Calculate and interpret a confidence interval for b based on a 95% confidence level.
=+a. Does the simple linear regression model specify a useful relationship between x and y?
=+b. Calculate an estimate of the average change in quit rate associated with a $1 increase in average hourly wage, and do so in a way that conveys information about the precision and reliability of
=+a. Based on the given P-value, does there appear to be a useful linear relationship between average wage and quit rate? Explain your reasoning.
=+s = 0.4862 R-sq = 72.9% R-sq(adj) = 70.8%Analysis of Variance Source DF SS MS F p Regression 1 8.2507 8.2507 34.90 0.000 Error 13 3.0733 0.2364 Total 14 11.3240
=+used to produce the accompanying MINITAB output The regression equation is quit rate = 4.86 – 0.347 wage Predictor Coef Stdev t-ratio p Constant 4.8615 0.5201 9.35 0.000 wage 0.34655 0.05866 5.91
=+13.18 Are workers less likely to quit their jobs when wages are high than when they are low? The paper “Investigating the Causal Relationship Between Quits and Wages: An Exercise in Comparative
=+c. Compute a 99% confidence interval for the true average change in oxygen consumption associated with a 1-min increase in exercise time.
=+what is the corresponding residual?
=+a 2-min exercise period. What amount of oxygen consumption would you predict for this exercise period, and
=+b. One sample observation on oxygen usage was 757 for
=+a. Estimate the slope and y intercept of the population regression line.
=+oxygen consumed during the exercise period resulted in the following summary statistics.
=+13.17 ▼ An experiment to study the relationship between x 5 time spent exercising (min) and y 5 amount of a 1y 2 y2 2 5 2401.85 a 1y 2 yˆ 2 2 5 561.46 a y 2 5 140,354 a xy 5 1387.20 a x 5 14.10
=+c. Obtain a 90% confidence interval forb, the average change in revenue associated with a $1000 (that is, 1-unit)increase in advertising expenditure.
=+b. Calculate se and sb.
=+a. What proportion of observed variation in sales revenue can be attributed to the linear relationship between revenue and advertising expenditure?
=+13.16 A study was carried out to relate sales revenue y(in thousands of dollars) to advertising expenditure x (also in thousands of dollars) for fast-food outlets during a 3-month period. A sample
=+c. Does the interval in Part (b) suggest that b has been precisely estimated? Explain.
=+b. Obtain a 95% confidence interval forb, the slope of the true regression line.
=+a. Calculate the estimated standard deviation of the statistic b.
=+13.15 Exercise 13.10 presented information from a study in which y was the hardness of molded plastic and x was the time elapsed since termination of the molding process.Summary quantities included
=+c. How many observations at each x value in Part (a) are required to yield a sb value that is half the value calculated in Part (a)? Verify your conjecture.
=+b. Now suppose that a second observation is made at every x value listed in Part (a) (for a total of 10 observations). Is the resulting value of sb half of what it was in Part (a)?
=+a. If s 5 4, what is the standard deviation of the statistic b?
=+13.13 Suppose that a single y observation is made at each of the x values 5, 10, 15, 20, and 25.
=+13.12 What is the difference between s and sb? What is the difference between sb and sb?
=+d. Calculate a point estimate of s. On how many degrees of freedom is your estimate based?
=+. How would you interpret this value?
=+b. Calculate the equation of the estimated regression line and use it to obtain the predicted market share when the advertising share is .09.c. Compute r 2
=+a. Construct a scatterplot for these data. Do you think the simple linear regression model would be appropriate for describing the relationship between x and y?
=+x .103 .072 .071 .077 .086 .047 .060 .050 .070 .052 y .135 .125 .120 .086 .079 .076 .065 .059 .051 .039
=+13.11 ● The accompanying data on x 5 advertising share and y 5 market share for a particular brand of cigarettes during 10 randomly selected years are from the article“Testing Alternative
=+b. What percentage of observed variation in hardness can be explained by the simple linear regression model relationship between hardness and elapsed time?
=+a. Calculate a point estimate of s. On how many degrees of freedom is the estimate based?
=+13.10 Exercise 5.48 described a regression situation in which y 5 hardness of molded plastic and x 5 amount of time elapsed since termination of the molding process. Summary quantities included n
=+. What is the number of degrees of freedom associated with this estimate?
=+b. Calculate the value of the estimated standard deviation se
=+a. What proportion of observed variation in total service time can be explained by a linear probabilistic relationship between total service time and the number of machines serviced?n 5 16 a 1y 2
=+13.9 The accompanying summary quantities resulted from a study in which x was the number of photocopy machines serviced during a routine service call and y was the total service time (min):
=+g. Calculate and interpret the value of se.
=+f. Calculate and interpret the value of r 2.
=+e. Should the model be used as a basis for predicting ski time when treadmill time is 15 min? Explain.
=+d. What would you predict ski time to be for an individual whose treadmill time is 10 min?
=+c. What is your estimate of the average change in ski time associated with a 1-min increase in treadmill time?
=+b. Determine the equation of the estimated regression line, and draw the line on your scatterplot.
=+a. Does a scatterplot suggest that the simple linear regression model is appropriate?
=+taken from the article “Physiological Characteristics and Performance of Top U.S. Biathletes” (Medicine and Science in Sports and Exercise [1995]: 1302–1310):x 7.7 8.4 8.7 9.0 9.6 9.6 y 71.0
=+13.8 ● The accompanying data on x 5 treadmill run time to exhaustion (min) and y 5 20-km ski time (min) were
=+d. Calculate a point estimate of true average residence half time when wind speed is 1 m/sec.
=+c. Estimate the mean change in residence half time associated with a 1-m/sec increase in wind speed.
=+b. Give a point estimate of s and interpret the estimate.
=+a. What percentage of observed variation in residence half time can be attributed to the simple linear regression model?
=+Uroleucon ambrosiae alatae on Bean Plants” (Environmental Entomology [1991]: 1375–1380) reported on a study in which aphids were placed on a bean plant, and the elapsed time until half of the
=+13.7 ▼ Legumes, such as peas and beans, are important crops whose production is greatly affected by pests. The article “Influence of Wind Speed on Residence Time of
=+d. Explain the difference between s and se.
=+c. Let x* denote a particular value of the independent variable. Explain the difference between a 1 bx* and a 1 bx*.
=+13.6a. Explain the difference between the line y 5 a 1 bx and the line 5 a 1 bx.b. Explain the difference between b and b.
=+b. What proportion of 1800-sq-ft homes would be priced over $110,000? Under $100,000?
=+a. What is the average change in price associated with one extra sq ft of space? With an additional 100 sq ft of space?
=+13.5 Suppose that a simple linear regression model is appropriate for describing the relationship between y 5 house price and x 5 house size (sq ft) for houses in a large city. The true regression
=+e. Interpret se in the context of this problem.

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