pls help! rate will be given! Write the solutions legibly!ENGINEERING DATA ANALYSIS An article in the Journal of the American Statistical Association ['Markov ChainMonte Carlo Methods for Computing Bayes Factors: A Comparative Review"(2001, Vol. 96, pp. 1122-1132)] analyzed the tabulated data on compressivestrength parallel to the grain versus resin-adjusted density for specimens of radiatapine. The data are shown below.Compressive DensityCompressive DensityStrengthStrength304029.2384030.7247024.7380032.7361032.3460032.6348031.3190022.1381031.5253025.3233024.5292030.8180019.9499038.9311027.3167022.1316027.1331029.2231024345030.1436033.8360031.4188021.5285026.7367032.2159022.1174022.5377030.3225027.5385032265025.6248023.2497034.5357030.3262026.2262029.9290026.7189020.8167021.1303033.2254024.1303028.2a. Fit a regression model relating compressive strength to density.b. Test for significance of regression with a = 0.05.c. Estimate o for this model.d. Calculate R² for this model. Provide an interpretation of this quantity.e. Prepare a normal probability plot of the residuals and interpret this display.f. Plot the residuals versus ŷ and versus x. Does the assumption of constantvariance seem to be satisfied?

The questions involves studying the relationship between compressive strength and density. The…

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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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Suppose that a worker’s productivity at manufacturing firms (prod) depends on two factors, hours of training (train) and worker’s efficiency. prod = a + b1 *train + b2 *efficiency + u Assume that this equation satisfies the Gauss-Markov assumptions. If less efficient workers tend to be required to take on-job-training, what is the likely bias in the estimated coefficient of train from the simple regression of prod on train? (i.e. is it under or overestimated) Please explain your answer.
Consider the fitted values from a simple linear regression model with intercept: yˆ = 7 + 4x. Assume that the total number of observations is n = 20. In addition, the explained sum of squares is SSE = 10 and the residual sum of squares is SSR = 30. Under the classical Gauss-Markov assumptions, a) What is the value of the R2 ?
Q. 6 What are the Gauss–Markov conditions that should hold for estimator to be BLUE ? Differentiate between Hetroskedasticty and multi-collinearity?
19. An article in International Journal of Electrical Power & Energy Systems "Stochastic Optimal Load Flow Using a Combined Quasi-Newton and Conjugate Gradient Technique" (1989, Vol. 11(2), pp. 85-93) considered the problem of optimal power flow in electric power systems and included the effects of uncertain variables in the problem formulation. The method treats the system power demand as a normal random variable with 0 mean and unit variance. What is the probability that the power demand is greater than -2 and less than 2? Round your answer to three decimal places (e.g. 98.765).
Determine the heteroscedasticity in a scatter plot?
The article “Effects of Diets with Whole Plant-Origin Proteins Added with Different Ratiosof Taurine:Methionine on the Growth, Macrophage Activity and Antioxidant Capacity ofRainbow Trout (Oncorhynchus mykiss) Fingerlings” (O. Hernandez, L. Hernandez, et al.,Veterinary and Animal Science, 2017:4-9) reports that a sample of 210 juvenile rainbowtrout fed a diet fortified with equal amounts of the amino acids taurine and methionine for aperiod of 70 days had a mean weight gain of 313 percent with a standard deviation of 25, while 210 fish fed with a control diet had a mean weight gain of 233 percent with a standard deviation of 19. Units are percent. Find a 99% confidence interval for the difference in weight gain on the two diets.
The shape of the mean-variance frontier that results from the combination of a riskless and arisky asset is…..:a. Is U-shaped, tilted 90 degrees clockwise.b. Is a straight line passing from the mean-variance points of the two assets.c. Is a hyperbola.d. Consists of two straight lines, each connecting one of the two assets to a risk-freeportfolio
14. an article in International Journal of Electrical Power & Energy Systems {"Stochastic Optimal Load Flow Using a Combined Quasi-Newton and Conjugate Gradient Technique" (1989, Vol. 11(2), pp. 85-93)} considered the problem of optimal power flow in electric power systems and included the effects of uncertain variables in the problem formulation. The method treats the system power demand as a normal random variable with 0 mean and unit variance. What is the power demand value that is exceeded with 80% probability? Round your answer to two decimal places (e.g. 98.76).
In running a regression model with heteroscedastic errors, the estimators given by Weighted Least Squares (WLS) are BLUE. However, we should still use OLS method with heteroskedasticity-robust standard errors because a) this remedial method is simpler. b) the Gauss-Markov theorem holds. c) the exact form of the conditional variance is rarely known in practice. d) many econometric softwares do not have a command for weighted least squares.
Suppose a researcher is interested inthe effectiveness in a new childhood exercise program implemented in a SRS of schools across a particular county. In order to test the hypothesis that the new program decreases BMI (Kg/m2), the researcher takes a SRS of children from schools where the program is employed and a SRS from schools that do not employ the program and compares the results. Assume the following table represents the SRSs of students and their BMIs. Student intervention group BMI (kg/m2) Student control group BMI (kg/m2) A 18.6 A 21.6 B 18.2 B 18.9 C 19.5 C 19.4 D 18.9 D 22.6 E 24.1 F 23.6 A) Assuming that all the necessary conditions are met (normality, independence, etc.) carry out the appropriate statistical test to determine if the new exercise program is effective. Use an alpha level of 0.05. Do not assume equal variances.B) Construct a 95% confidence interval about your estimate for the average difference in BMI between the groups.
For the horseshoe crab data with width, colors, and spine as predictors, suppose you start a backward elimination process with the most complex model possible Denoted by C ∗ S ∗ W, it uses main effects for each term as well as the three two-factor interactions and the three-factor interaction Conduct a likelihood-ratio test comparing this model to the simpler model that removes the three-factor interaction term but has all the two-factor interactions. Does this suggest that the three-factor term can be removed from the model? At the next stage, if we were to drop one term, explain why we would select model C ∗ S + C ∗ W
Distinguish between Heteroskedasticity and autocorrelation

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