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introduction to probability statistics

Probability And Statistics For Engineering And The Sciences 8th Edition Jay L Devore, Roger Ellsbury - Solutions

Coir fiber, derived from coconut, is an eco-friendly material with great potential for use in construction. The article“Seepage Velocity and Piping Resistance of Coir Fiber Mixed Soils” (J. of Irrig. and Drainage Engr., 2008:485–492) included several multiple regression analyses.The
The article “Sensitivity Analysis of a 2.5 kW Proton Exchange Membrane Fuel Cell Stack by Statistical Method” (J. of Fuel Cell Sci. and Tech., 2009: 1–6) used regression analysis to investigate the relationship between fuel cell power (W) and the independent variables , , and .a. Here is
The article “Chemithermomechanical Pulp from Mixed High Density Hardwoods” (TAPPI, July 1988: 145–146)reports on a study in which the accompanying data was obtained to relate to NaOH used as a pretreatment chemical and time (min) for a batch of pulp.x1 x2 y 3 30 5.95 3 60 5.60 3 90 5.44 9 30
The effect of manganese (Mn) on wheat growth is examined in the article “Manganese Deficiency and Toxicity Effects on Growth, Development and Nutrient Composition in Wheat” (Agronomy J., 1984: 213–217). A quadratic regression model was used to relate height (cm) to, with mM as the units for
Conductivity is one important characteristic of glass. The article “Structure and Properties of Rapidly Quenched Li2O-Al2ONb2O5 Glasses” (J. of the Amer. Ceramic Soc., 1983: 890–892)202.88 sYˆ 5 .1141 x 5 100 bˆ2 5 2.00163141, sbˆ2 5 .00003391, SSE 5 .29, SST 5 bˆ0 5 21.5127, bˆ1 5
The accompanying data on and power (W) for a certain laser configuration was read from a graph in the article “Frequency Dependence in RF Discharge Excited Waveguide CO2 Lasers” (IEEE J. of Quantum Electronics, 1984: 509–514).x | 60 63 77 100 125 157 186 222 y | 16 17 19 21 22 20 15 5 A
The article “An Experimental Study of Resistance Spot Welding in 1 mm Thick Sheet of Low Carbon Steel” (J. of Engr. Manufacture, 1996: 341–348) discussed a statistical analysis whose basic aim was to establish a relationship that could explain the variation in weld strength (y) by relating
An ammonia bath is the one most widely used for depositing Pd-Ni alloy coatings. The article “Modelling of Palladium and Nickel in an Ammonia Bath in a Rotary Device” (Plating and Surface Finishing, 1997: 102–104)reported on an investigation into how bath-composition characteristics affect
An aeronautical engineering student carried out an experiment to study how ratio related to the variables of a certain forward lifting surface relative to the main wing and placement relative to the main wing, obtaining the following data (Statistics for Engineering Problem Solving, p. 133):a.
Feature recognition from surface models of complicated parts is becoming increasingly important in the development of efficient computer-aided design (CAD) systems.The article “A Computationally Efficient Approach to Feature Abstraction in Design-Manufacturing Integration”(J. of Engr. for
The article “Validation of the Rockport Fitness Walking Test in College Males and Females” (Research Quarterly for Exercise and Sport, 1994: 152–158) recommended the following estimated regression equation for relating (L/min, a measure of cardiorespiratory fitness) to the predictors, and
The authors of the article “Long-Term Effects of Cathodic Protection on Prestressed Concrete Structures” (Corrosion, 1997: 891–908) presented a scatter plot of permeation flux (mA/cm2) versus foil thickness(cm1); the substantial linear pattern was used as a basis for an important conclusion
Refer to the water-discharge data given in Exercise 55 and let , and . Consider fitting the model .a. The resulting hii’s are .138, .302, .266, .604, .464, .360,.215, .153, .214, and .284. Does any observation appear to be influential?b. The estimated coefficients are and , and the corresponding
A study carried out to investigate the relationship between a response variable relating to pressure drops in a screen-plate bubble column and the predictors fluid velocity, viscosity, and mesh size resulted in the accompanying data (“A Correlation of TwoPhase Pressure Drops in Screen-Plate
For each method, explain what occurred at every iteration of the algorithm
The accompanying Minitab output resulted from applying both the backward elimination method and the forward selection method to the wood specific gravity data referred to in Exercise
Minitab’s Best Regression option was used on the wood specific gravity data referred to in Exercise 56, resulting in the accompanying output. Which model(s) would you recommend for investigating in more detail?
The article “Response Surface Methodology for Protein Extraction Optimization of Red Pepper Seed” (Food Sci. and Tech., 2010: 226–231) gave data on the response variable and the independent variables and .a. Fitting the model with the four xi’s as predictors gave the following
In the accompanying table, we give the smallest SSE for each number of predictors for a regression problem in which heat of hardening in cement, tricalcium aluminate, tricalcium silicate, aluminum ferrate, and dicalcium silicate.Number of Predictors k Predictor(s) SSE 1 x4 880.85 2 x1, x2 58.01 3
In an experiment to study factors influencing wood specific gravity (“Anatomical Factors Influencing Wood Specific Gravity of Slash Pines and the Implications for the Development of a High-Quality Pulpwood,” TAPPI, 1964:401–404), a sample of 20 mature wood samples was obtained, and
The article “Bank Full Discharge of Rivers” (Water Resources J., 1978: 1141–1154) reports data on discharge amount (q, in m3/sec), flow area (a, in m2), and slope of the water surface (b, in m/m) obtained at a number of floodplain stations. A subset of the data follows. The article proposed a
The use of high-strength steels (HSS) rather than aluminum and magnesium alloys in automotive body structures reduces vehicle weight. However, HSS use is still problematic because of difficulties with limited formability, increased springback, difficulties in joining, and reduced die life. The
Snowpacks contain a wide spectrum of pollutants that may represent environmental hazards. The article “Atmospheric PAH Deposition: Deposition Velocities and Washout Ratios” (J. of Environmental Engineering, 2002: 186–195)focused on the deposition of polyaromatic hydrocarbons.The authors
Utilization of sucrose as a carbon source for the production of chemicals is uneconomical. Beet molasses is a readily available and low-priced substitute. The article “Optimization of the Production of b-Carotene from Molasses by Blakeslea Trispora (J. of Chem. Tech. and Biotech. 2002: 933–943)
The article “The Undrained Strength of Some Thawed Permafrost Soils” (Canadian Geotechnical J., 1979:420–427) contains the following data on undrained shear strength of sandy soil (y, in kPa), depth (x1, in m), and water The predicted values and residuals were computed by fitting a full
a. When the model is fit to the hops data of Exercise 49, the estimate of b5 is with estimated standard deviation . Test versus.b. Each t ratio for the model of part(a) is less than 2 in absolute value, yet for this model. Would it be correct to drop each term from the model because of its small
The article “The Influence of Temperature and Sunshine on the Alpha-Acid Contents of Hops (Agric. Meteor. 1974:375–382) reports the following data on yield (y), mean temperature over the period between date of coming into hops and date of picking (x1), and mean percentage of sunshine during the
An experiment to investigate the effects of a new technique for degumming of silk yarn was described in the article “Some Studies in Degumming of Silk with Organic Acids” (J. Society of Dyers and Colourists, 1992: 79–86). One response variable of interest was . The experimenters made
Efficient design of certain types of municipal waste incinerators requires that information about energy content of the waste be available. The authors of the article “Modeling the Energy Content of Municipal Solid Waste Using Multiple Regression Analysis” (J. of the Air and Waste Mgmnt.Assoc.,
A regression analysis carried out to relate for a water filtration system (hr) to since the previous service (months) and of repair (1 if electrical and 0 if mechanical) yielded the following model based on observations: . In addition, , and .a. Does there appear to be a useful linear relationship
The accompanying Minitab regression output is based on data that appeared in the article “Application of Design of Experiments for Modeling Surface Roughness in Ultrasonic Vibration Turning” (J. of Engr. Manuf., 2009: 641–652).The response variable is surface roughness (mm), and the
An experiment carried out to study the effect of the mole contents of cobalt (x1) and the calcination temperature (x2)on the surface area of an iron-cobalt hydroxide catalyst (y)resulted in the accompanying data (“Structural Changes and Surface Properties of Spinels,” J. of Chemical Tech. and
An investigation of a die-casting process resulted in the accompanying data on ,, and difference on the die surface (“A Multiple-Objective Decision-Making Approach for Assessing Simultaneous Improvement in Die Life and Casting Quality in a Die Casting Process,” Quality Engineering, 1994:
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. The article “Prediction of Rarities from Habitat Variables: Coastal Plain Plants on Nova Scotian
The article “Readability of Liquid Crystal Displays: A Response Surface” (Human Factors, 1983: 185–190) used a multiple regression model with four independent variables to study accuracy in reading liquid crystal displays. The variables were digit The model fit to data was. The resulting
Let at a fast-food outlet (1000s of $), of competing outlets within a 1-mile radius, within a 1-mile radius (1000s of people), and x3 be an indicator variable that equals 1 if the outlet has a drive-up window and 0 otherwise. Suppose that the true regression model isa. What is the mean value of
Let life of a bearing, , and. Suppose that the multiple regression model relating life to viscosity and load isa. What is the mean value of life when viscosity is 40 and load is 1100?b. When viscosity is 30, what is the change in mean life associated with an increase of 1 in load? When viscosity is
A trucking company considered a multiple regression model for relating the dependent variable daily travel time for one of its drivers (hours) to the predictors traveled (miles) and of deliveries made. Suppose that the model equation isa. What is the mean value of travel time when distance traveled
Cardiorespiratory fitness is widely recognized as a major component of overall physical well-being. Direct measurement of maximal oxygen uptake (VO2max) is the single best measure of such fitness, but direct measurement is time-consuming and expensive. It is therefore desirable to have a prediction
The article “The Respiration in Air and in Water of the Limpets Patella caerulea and Patella lusitanica” (Comp.Biochemistry and Physiology, 1975: 407–411) proposed a simple power model for the relationship between respiration rate y and temperature x for P. caerulea in air. However, a plot of
The following data resulted from an experiment to assess the potential of unburnt colliery spoil as a medium for plant growth. The variables are extractable cations and acidity/total cation exchange capacity(“Exchangeable Acidity in Unburnt Colliery Spoil,” Nature, 1969: 161):x 23 5 16 26 30 38
In many polynomial regression problems, rather than fitting a “centered” regression function using , computational accuracy can be improved by using a function of the standardized independent variable, where sx is the standard deviation of the xi’s. Consider fitting the cubic regression
The following data is a subset of data obtained in an experiment to study the relationship between x 5 soil pH and. Concentration/EC (“Root Responses of Three Gramineae Species to Soil Acidity in an Oxisol and an Ultisol,” Soil Science, 1973: 295–302):x 4.01 4.07 4.08 4.10 4.18 y 1.20 .78 .83
The accompanying data on output (W) and difference (°K) was provided by the authors of the article “Comparison of Energy and Exergy Efficiency for Solar Box and Parabolic Cookers” (J. of Energy Engr., 2007: 53–62).The article’s authors fit a cubic regression model to the data.Here is
The accompanying data was extracted from the article“Effects of Cold and Warm Temperatures on Springback of Aluminum-Magnesium Alloy 5083-H111” (J. of Engr.Manuf., 2009: 427–431). The response variable is yield strength (MPa), and the predictor is temperature (°C).x 50 25 100 200 300 y 91.0
High-alumina refractory castables have been extensively investigated in recent years because of their significant advantages over other refractory brick of the same class—lower production and application costs, versatility, and performance at high temperatures. The accompanying data on and was
The viscosity (y) of an oil was measured by a cone and plate viscometer at six different cone speeds (x). It was assumed that a quadratic regression model was appropriate, and the estimated regression function resulting from the observations wasa. Estimate , the expected viscosity when speed is 75
The following data on concentration (g/L) and time (days) for a particular blend of malt liquor was read from a scatter plot in the article “Improving Fermentation Productivity with Reverse Osmosis” (Food Tech., 1984: 92–96):x 1 2 34 56 7 8 y 74 54 52 51 52 53 58 71a. Verify that a scatter
The article “Physical Properties of Cumin Seed” (J. of Agric.Engr. Res., 1996: 93–98) considered a quadratic regression of density on y 5 bulk x 5 moisture content. Data from a graph in the article follows, along with Minitab output from the quadratic fit The regression equation is Predictor
The article “Acceptable Noise Levels for Construction Site Offices” (Building Serv. Engr. Res. Tech., 2009:87–94) analyzed responses from a sample of 77 individuals, each of whom was asked to say whether a particular noise level (dBA) to which he/she had been exposed was acceptable or
Kyphosis refers to severe forward flexion of the spine following corrective spinal surgery. A study carried out to determine risk factors for kyphosis reported the accompanying ages (months) for 40 subjects at the time of the operation; the first 18 subjects did have kyphosis and the remaining 22
Suppose x and y are related according to a probabilistic exponential model , with a constant independent of x (as was the case in the simple linear model. Is V(Y) a constant independent of x [as was the case for , where ]?Explain your reasoning. Draw a picture of a prototype scatter plot resulting
In each of the following cases, decide whether the given function is intrinsically linear. If so, identify x and y, and then explain how a random error term can be introduced to yield an intrinsically linear probabilistic model.a.b.c.d.
A plot in the article “Thermal Conductivity of Polyethylene:The Effects of Crystal Size, Density, and Orientation on the Thermal Conductivity” (Polymer Engr. and Science, 1972:204–208) suggests that the expected value of thermal conductivity y is a linear function of , where x is lamellar
Polyester fiber ropes are increasingly being used as components of mooring lines for offshore structures in deep water.The authors of the paper “Quantifying the Residual Creep Life of Polyester Mooring Ropes” (Intl. J. of Offshore and Polar Exploration, 2005: 223–228) used the accompanying
Failures in aircraft gas turbine engines due to high cycle fatigue is a pervasive problem. The article “Effect of Crystal Orientation on Fatigue Failure of Single Crystal Nickel Base Turbine Blade Superalloys” (J. of Engineering for Gas Turbines and Power, 2002: 161–176)gave the accompanying
No tortilla chip aficionado likes soggy chips, so it is important to find characteristics of the production process that produce chips with an appealing texture. The following data on time (sec) and content (%)appeared in the article “Thermal and Physical Properties of Tortilla Chips as a
If there is at least one x value at which more than one observation has been made, there is a formal test procedure for testing for some values , (the true regression function is linear)versus Ha: H0 is not true (the true regression function is not linear)Suppose observations are made at . Let
Consider the following four (x, y) data sets; the first three have the same x values, so these values are listed only once(Frank Anscombe, “Graphs in Statistical Analysis,”Amer.Statistician, 1973: 17–21)has a standard normal distribution. If is substituted for s, the resulting variable has a
Recall that has a normal distribution with expected value and variance so that Z 5 bˆ0 1 bˆ1x 2 (b0 1 b1x)s° 1 n1 (x 2 x) 2 g(xi 2 x) 2 ¢1/2 s2 • 1 n1 (x 2 x) 2 g(xi 2 x) 2¶b0 1 b1x bˆ0 1 bˆ1x V(Yi 2 Yˆi)V(Yˆi x )V(Yˆ)Yi 5 Yˆi 1 (Yi 2 Yˆi)Yi 2 Yˆ Y i ˆi V(Yi 2 Yˆi)gcj Yj Yˆi 5
a. Express the ith residual (where )in the form , a linear function of the Yj’s. Then use rules of variance to verify that is given by Expression (13.2).b. It can be shown that and (the ith predicted value and residual) are independent of one another. Use this fact, the relation , and the
a. Show that when the ei’s are the residuals from a simple linear regression.b. Are the residuals from a simple linear regression independent of one another, positively correlated, or negatively correlated? Explain.c. Show that for the residuals from a simple linear regression. (This result along
Continuous recording of heart rate can be used to obtain information about the level of exercise intensity or physical strain during sports participation, work, or other daily activities. The article“The Relationship Between Heart Rate and Oxygen Uptake During Non-Steady State Exercise”
The accompanying scatter plot is based on data provided by authors of the article “Spurious Correlation in the USEPA Rating Curve Method for Estimating Pollutant Loads” (J. of Envir. Engr., 2008: 610–618); here discharge is in ft3/s as opposed to m3/s used in the article. The point on the far
As the air temperature drops, river water becomes supercooled and ice crystals form. Such ice can significantly affect the hydraulics of a river. The article “Laboratory Study of Anchor Ice Growth” (J. of Cold Regions Engr., 2001: 60–66)described an experiment in which ice thickness (mm) was
Wear resistance of certain nuclear reactor components made of Zircaloy-2 is partly determined by properties of the oxide layer. The following data appears in an article that proposed a new nondestructive testing method to monitor thickness of the layer (“Monitoring of Oxide Layer Thickness on
Example 12.6 presented the residuals from a simple linear regression of moisture content y on filtration rate x.a. Plot the residuals against x. Does the resulting plot suggest that a straight-line regression function is a reasonable choice of model? Explain your reasoning.b. Using , compute the
Suppose the variables and time are related according to the simple linear regression model with .a. If observations are made at the x values x1 5 5, x2 5 10, x2 5 15, x2 5 20, and , calculate the standard deviations of the five corresponding residuals.b. Repeat part (a) for , and . x 5 5 50 x 1 5
Reconsider the situation of Exercise 73, in which x retained austenite content using a garnet abrasive and y abrasive wear loss were related via the simple linear regression model . Suppose that for a second type of abrasive, these variables are also related via the simple linear regression model
In biofiltration of wastewater, air discharged from a treatment facility is passed through a damp porous membrane that causes contaminants to dissolve in water and be transformed into harmless products. The accompanying data on x inlet temperature (°C) and y removal efficiency (%)was the basis for
Use the formula for computing SSE to verify that.
Verify that the t statistic for testing in Section 12.3 is identical to the t statistic in Section 12.5 for testing.
Let sx and sy denote the sample standard deviations of the observed x’s and y’s, respectively [that is, and similarly for ].a. Show that an alternative expression for the estimated regression line isb. This expression for the regression line can be interpreted as follows. Suppose . What then is
Show that , which gives an alternative computational formula for SSE.
In Section 12.4, we presented a formula for and a CI for . Taking gives and a CI for b0. Use the data of Example 12.11 to calculate the estimated standard deviation of and a 95% CI for the y-intercept of the true regression line.
The article “Photocharge Effects in Dye Sensitized Ag[Br,I]Emulsions at Millisecond Range Exposures” (Photographic Sci. and Engr., 1981: 138–144) gives the accompanying data on light absorption at 5800 A and y peak photovoltage.x 5a. Construct a scatter plot of this data. What does it
An investigation was carried out to study the relationship between speed (ft/sec) and stride rate (number of steps taken/sec) among female marathon runners. Resulting summary quantities included, and .a. Calculate the equation of the least squares line that you would use to predict stride rate from
The accompanying data was read from a scatter plot in the article “Urban Emissions Measured with Aircraft” (J. of the Air and Waste Mgmt. Assoc., 1998: 16–25). The response variable is , and the explanatory variable is . CONOy a 5 .01 CO 50 60 95 108 135 2.3 4.5 4.0 3.7 8.2 CO 210 214 315
The SAS output at the bottom of this page is based on data from the article “Evidence for and the Rate of Denitrification in the Arabian Sea” (Deep Sea Research, 1978: 431–435). The variables under study are x salinity level (%) and y nitrate level (mM/L).a. What is the sample size n? [Hint:
The accompanying data on x diesel oil consumption rate measured by the drain–weigh method and y rate measured by the CI-trace method, both in g/hr, was read from a graph in the article “A New Measurement Method of Diesel Engine Oil Consumption Rate” (J. of Soc. of Auto Engr., 1985: 28–33).x
Forensic scientists are often interested in making a measurement of some sort on a body (alive or dead) and then using that as a basis for inferring something about the age of the body. Consider the accompanying data on age (yr) and% D-aspertic acid (hereafter %DAA) from a particular tooth(“An
The appraisal of a warehouse can appear straightforward compared to other appraisal assignments. A warehouse appraisal involves comparing a building that is primarily an open shell to other such buildings. However, there are still a number of warehouse attributes that are plausibly related to
A sample of pairs was collected and a test of versus was carried out. The resulting P-value was computed to be .00032.a. What conclusion would be appropriate at level of significance .001?b. Does this small P-value indicate that there is a very strong linear relationship between x and y (a value of
Consider a time series—that is, a sequence of observations obtained over time—with observed values . Suppose that the series shows no upward or downward trend over time. An investigator will frequently want to know just how strongly values in the series separated by a specified number of time
Torsion during hip external rotation and extension may explain why acetabular labral tears occur in professional athletes. The article “Hip Rotational Velocities During the Full Golf Swing” (J. of Sports Science and Med., 2009: 296–299)Ha H0: r 5 2.5 : r , 2.5 gxi y g(yi 2 y) i 5 16,731 2 5
The article “Increases in Steroid Binding Globulins Induced by Tamoxifen in Patients with Carcinoma of the Breast” (J.of Endocrinology, 1978: 219–226) reports data on the effects of the drug tamoxifen on change in the level of cortisol-binding globulin (CBG) of patients during treatment.With
Hydrogen content is conjectured to be an important factor in porosity of aluminum alloy castings. The article “The SReduced Pressure Test as a Measuring Tool in the Evaluation of Porosity/Hydrogen Content in A1–7 Wt Pct Si-10 Vol Pct SiC(p) Metal Matrix Composite” (Metallurgical Trans., 1993:
The authors of the paper “Objective Effects of a Six Months’ Endurance and Strength Training Program in Outpatients with Congestive Heart Failure” (Medicine and Science in Sports and Exercise, 1999: 1102–1107) presented a correlation analysis to investigate the relationship between maximal
Head movement evaluations are important because individuals, especially those who are disabled, may be able to operate communications aids in this manner. The article “Constancy gyi 5 47.92, gyi 2 5 130.6074, gxi yi 5 5530.92 nof Head Turning Recorded in Healthy Young Humans”(J. of Biomed.
Toughness and fibrousness of asparagus are major determinants of quality. This was the focus of a study reported in“Post-Harvest Glyphosphate Application Reduces Toughening, Fiber Content, and Lignification of Stored Asparagus Spears” (J. of the Amer. Soc. of Hort. Science, 1988: 569–572).The
The article “Bone Density and Insertion Torque as Predictors of Anterior Cruciate Ligament Graft Fixation Strength” (The Amer. J. of Sports Med., 2004: 1421–1429)gave the accompanying data on maximum insertion torque and yield load (N), the latter being one measure of graft strength, for 15
Verify that is indeed given by the expression in the text. [Hint: .]
The decline of water supplies in certain areas of the United States has created the need for increased understanding of relationships between economic factors such as crop yield and hydrologic and soil factors. The article “Variability of Soil Water Properties and Crop Yield in a Sloped
Plasma etching is essential to the fine-line pattern transfer in current semiconductor processes. The article “Ion BeamAssisted Etching of Aluminum with Chlorine” (J. of the Electrochem. Soc., 1985: 2010– 2012) gives the accompanying data (read from a graph) on chlorine flow (x, in SCCM)
Refer to Example 12.12 in which x test track speed and y rolling test speed.a. Minitab gave and . Why is the former estimated standard deviation smaller than the latter one?sbˆ01bˆ1 s (47) 5 .186 bˆ01bˆ1(45) 5 .120 S 5 0.0737573 R–Sq 5 80.2% R–Sq(adj) 5 78.4%Fermi pos 5 0.7217 2 0.4327 n 5
Silicon-germanium alloys have been used in certain types of solar cells. The paper “Silicon-Germanium Films Deposited by Low-Frequency Plasma-Enhanced Chemical Vapor Deposition” (J. of Material Res., 2006: 88–104) reported on a study of various structural and electrical properties. Consider
The catch basin in a storm-sewer system is the interface between surface runoff and the sewer. The catch-basin insert is a device for retrofitting catch basins to improve pollutantremoval properties. The article “An Evaluation of the Urban Stormwater Pollutant Removal Efficiency of Catch Basin
The simple linear regression model provides a very good fit to the data on rainfall and runoff volume given in Exercise 16 of Section 12.2. The equation of the least squares line is, and .a. Use the fact that when rainfall volume is 40 m3 to predict runoff in a way that conveys information about
Astringency is the quality in a wine that makes the wine drinker’s mouth feel slightly rough, dry, and puckery. The paper “Analysis of Tannins in Red Wine Using Multiple Methods: Correlation with Perceived Astringency” (Amer. J.of Enol. and Vitic., 2006: 481–485) reported on an
Reconsider the filtration rate–moisture content data introduced in Example 12.6 (see also Example 12.7).a. Compute a 90% CI for , true average moisture content when the filtration rate is 125.b. Predict the value of moisture content for a single experimental run in which the filtration rate is

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