12-6. A regression model is to be developed for predictingthe ability of soil to absorb chemical contaminants. Ten obser-vations have been taken on a soil absorption index (y) and tworegressors: x₁ = amount of extractable iron ore and x₂ = amountof bauxite. We wish to fit the model y = Bo + B₁ x₁ + B₂x₂ + €.Some necessary quantities are:1.17991-7.30982 E-37.3006 E-4(X'X)¹ = -7.30982 E-37.9799 E-5-1.23713 E-4,7.3006 E-4 -1.23713 E-44.6576 E-4220X'y = 36,7689,965(a) Estimate the regression coefficients in the model specified.(b) What is the predicted value of the absorption index y whenx₁ = 200 and x₂ = 50?

Answered: Image /qna-images/answer/efca2537-964a-4a2f-bbd5-9715285203ce.jpg

Answered: 12-6. A regression model is to be…

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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The data in worksheet 2.2 have spec limits USL/LSL = 40 ± 1. Perform the process capability analysis (Cp, Cpk, Pp, and Ppk) and diagnose the process, i.e. what problems are present? What steps should be taken to improve the process and how effective will they be?
3
The article "The Undrained Strength of Some Thawed Permafrost Soils" contained the accompanying data on the following. y shear strength of sandy soil (kPa) x₂-depth (m) x₂ water content (%) The predicted values and residuals were computed using the estimated regression equation 9-145.41-14.24x, +12.70x₂ +0.079x,-0.236 +0.441x where x₂-x₂²x₂-x₂², and x ₁2 Y 14.7 *2 9.1 31.6 48.0 36.5 27.1 25.6 36.7 25.8 10.0 6.0 39.2 16.0 7.0 39.3 16.8 7.0 38.4 20.7 7.4 34.0 38.8 8.3 33.7 16.9 6.4 28.0 27.0 8.1 33.0 16.0 4.6 26.4 24.9 9.8 37.9 7.3 2.8 34.5 12.8 1.9 36.3 Predicted y Residual 23.83 47.07 26.46 10.77 14.57 16.88 23.38 25.07 16.23 24.31 15.06 28.64 15.08 8.15 -9.13 0.93 -0.86 -0.77 1.43 -0.08 -2.68 13.73 0.67 2.69 0.94 -3.74 -7.78 4.65 (a) Use the given information to calculate SSResid, SSTO, and SSRegr. (Round your answers to four decimal places.) SSTO- 1x |x SSResid- SSRegr - Ix (b) Calculate R² for this regression model. (Round your answer to three decimal places.) R²-X How would you…
The price X (dollars per pound) and consumption y (in pounds per capita) of beef were samples for 10 randomly selected years. The following data should be used to answer the question that follows. n = 10 Ex = 36.19 Ex2 = 134.17 2.9 < x s 6.2 Ey = 774.7 Iy² = 60739.23 Exy = 2832.21 Before the slope of the line of best fit can be estimated, it is necessary to calculate SS Enter the value for SSx accurate to the nearest tenth.
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Suppose that the true relationship between y; and ; is as follows, Yi = B₁ + B₂xi + Ui The error term satisfies that E[u₂] = 0 and Var(u) = 1. You find another variable zi whose sample correlation with x is equal to -1. Select correct statement(s). Because the correlation is equal to -1, we have %₁ = -₂. O If we add z; in the regression model along with ;, R² will be increased. Adding z; along with in the regression model is not plausible because of the perfect multicollinearity. O If we estimate the model y₁ = a₁ + a2%; + e₁, the estimator of a2 will be equal to -3₂, where B₂ is the OLS estimator of 32
1. Supercavitation is a propulsion technology for undersea vehicles that can greatly increase their speed. It occurs above approximately 50 meters per second when pressure drops sufficiently to allow the water to dissociate into water vapor, forming a gas bubble behind the vehicle. When the gas bubble completely encloses the vehicle, supercavitation is said to occur. Eight tests were conducted on a scale model of an undersea vehicle in a towing basin with the average observed speed x = 102.2 meters per second. Assume that speed is normally distributed with known standard deviation o =4 meters per second. 1.1. Test the hypothesis H0 : µ=100 versus H1: µ < 100 using a=0.05. 1.2. What is the P-value for the test in part 1.1.? 1.3. Compute the type II error if the true mean speed is as low as 95 meters per second. 1.4. What sample size would be required to detect a true mean speed as low as 95 meters per second if you are willing to accept a type Il error of 0.15?
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