5.1 Byers and Williams (Viscosities of Binary and Ternary Mixtures of PolyaromaticHydrocarbons," Journal of Chemical and Engineering Data, 32, 349 – 354, 1987)studied the impact of temperature (the regressor) on the viscosity (the response) oftoluene- tetralin blends. The following table gives the data for blends with a 0.4 molarfraction of toluene.Temperature (°C)Viscosity (mPa·s)1.13324.935.00.977244.90.853255.10.755065.20.672375.20.602185.20.542095.20.5074b. Fit the straight line model. Compute the summary statistics and the residual plots.What are your conclusions regarding model adequacy?

Given Information: Consider the given data: Temperature Viscosity 24.9 1.133 35 0.9772 44.9…

Answered: 5.1 Byers and Williams (Viscosities of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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4. Captopril is a drug designed to lower systolic blood pressure. When subjects were treated with this drug, their systolic blood pressure readings (in mm Hg) were measured before and after the drug was taken. Results are given in the accompanying table (based on data from “Essential Hypertension: Effect of an Oral Inhibitor of Angiotensin-Converting Enzyme”, by MacGregor et al., BMJ, Vol. 2). Using a 0.01 significance level, is there sufficient evidence to support the claim that captopril has an effect on systolic blood pressure? Explain why statistical methods from Z-interval, Z-test, T-interval or T-test –cannot be used for this problem. Then, use the sign test to conduct the required test in R studio. Please show your work.
The cetane number is a critical property in specifying the ignition quality of a fuel used in a diesel engine. Determination of this number for a biodiesel fuel is expensive and time- consuming. The article "Relating the Cetane Number of Biodiesel Fuels to Their Fatty Acid Composition: A Critical Study" (J. of Automobile Engr., 2009: 565–583) included the following data on x = iodine value (g) and y = cetane number for a sample of 15 biofuels The iodine value (x) is the amount of iodine necessary to saturate a sample of 100 g of oil. The article's authors fit the simple linear regression model to this data, so let' s does the same. 132.0 129.0 120.0 113.2 105.0 92.0 84.0 88.4 59.0 80.0 81.0 81.5 71.0 69.2 63.0 y 46.0 48.0 51.0 52.1 54.0 52.0 59.0 58.7 61.6 64.0 61.4 54.6 58.8 58.0 51.4 3) Estimate the correlation coefficient (Pearson coefficient), r, between x and y and explain briefly the strength of r and its direction and comment the p-value. 4) Construct a 95% two-sided confidence…
9
Mist (airborne droplets or aerosols) is generated when metal- removing fluids are used in machining operations to cool and lubricate the tool and workpiece. Mist generation is a concern to OSHA, which has recently lowered substantially the workplace standard. The article "Variables Affecting Mist Generaton from Metal Removal Fluids" (Lubrication Engr., 2002: 10-17) gave the accompanying data on x = fluid-flow velocity for a 5% soluble oil (cm/sec) and y = the extent of mist droplets having diameters smaller than 10 μm (mg/m³): x y 89 177 189 354 362 442 965 .40 .60 .48 .66 .61 .69 .99 a. The investigators performed a simple linear regres- sion analysis to relate the two variables. Does a scat- terplot of the data support this strategy? b. What proportion of observed variation in mist can be attributed to the simple linear regression relationship between velocity and mist? c. The investigators were particularly interested in the impact on mist of increasing velocity from 100 to 1000 (a…
A researcher conducts a two-year study comparing the number of cavities in a group of 30 randomly selected young children from the community before and after the application of fluoride to test if there is a decrease in the number of cavities. This is an example of a/an: Independent-samples t test or Dependent-samples t test?
The article "Oxidation State and Activities of Chromium Oxides in Cao-SiO,-CrO, Slag System" (Y. Xiao, L. Holappa, and M. Reuter, Metallurgical and Materials Transactions B, 2002:595-603) presents the amount x (in mole percent) and activity coefficient y of CrO,5 for several specimens. The data, extracted from a larger table, are presented in the following table. х У 2.6 10.20 5.03 19.9 8.84 0.8 6.62 5.3 2.89 20.3 2.31 39.4 7.13 5.8 3.40 29.4 5.57 2.2 7.23 5.5 2.12 33.1 1.67 44.2 5.33 13.1 16.70 0.6 9.75 2.2 2.74 16.9 2.58 35.5 1.50 48.0 Compute the least-squares line for predicting y from x. b. Plot the residuals versus the fitted values. Compute the least-squares line for predicting y from 1/x. d. Plot the residuals versus the fitted values. C. Using the better fitting line, find a 95% confidence interval for the mean value of y when x= 5.0.
18. Because ethanol contains less energy than gasoline, a researcher wants to determine if the mileage of a car (y) is affected by the percent ethanol in the gasoline (x). The true population regression line relating the mean mileage y for a given ethanol content x (in percent) is μy|x = β0 + β1x. In a controlled environment, the mileage of a car is recorded when refueled 7 times using between 0% and 10% ethanol. The least squares regression line was found to be yˆ = βˆ0 + βˆ1x = 32.96 − 0.250x. We wish to test H0 : β1 = 0 versus Ha : β1 < 0 at the α = 0.05 significance level (i.e. we want to determine if the addition of ethanol significantly decreases mean gas mileage). What is the p−value for this test? What is your conclusion? Note: s?e(βˆ1) = 0.0485. Which of the following is/are true? (A) In reference to question (18), it would be appropriate to approximate the mean mileage when the car is using 85% ethanol (B) In reference to question (18), a 95% confidence interval for β1…

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