An article in International Journal of Electrical Power & Energy Systems ["Stochastic Optimal Load Flow Using a Combined Quasi-Newtonand Conjugate Gradient Technique" (1989, Vol. 11(2), pp. 85-93)] considered the problem of optimal power flow in electric powersystems and included the effects of uncertain variables in the problem formulation. The method treats the system power demand as anormal random variable with 0 mean and unit variance.(a) What is the power demand value that is exceeded with 80% probability?Round your answer to two decimal places (e.g. 98.76).a =i(b) What is the probability that the power demand is positive?P =i

Answered: Image /qna-images/answer/c531200a-6fad-46dc-9131-e093e751bc03.jpg

Answered: An article in International Journal 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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An experiment was run and the following data table was produced: (a) Calculate the correlation coefficient for the data. Is the data positivelyor negatively correlated, and is that correlation weak, moderate, or strong?(b) Find the equation of the least squares regression line and plot the lineon top of a scatterplot of the data.
Consider the following regression model: Yi = B1 + B2X2i + ß3X3i + ß4X4i + ui Using the model above show that the maximum likelihood estimator for the variance, var (ui||X2i, X3i, B4X4i), is biased (be sure to comment of the nature of the bias).
In a production process, the time (in minutes) taken (run time) for a production run and the number of items produced (run size) for 15 randomly selected orders are analyzed using Minitab statistical software. The Minitab output is as follows: Regression Analysis: Run time versus Run size Analysis of Variance Source DF Adj SS Adj MS F-Value Critical value Regression 1 8737.1 8737.1 29.35 ……… Error 13 3870.5 297.7 Total 14 12607.6 Model Summary S R-sq R-sq(adj) R-sq(pred) 17.2549 ……. 66.94% 61.32% Coefficients Term Coef SE Coef T-Value P-Value VIF Constant 148.4 11.3 13.13 0.000 Run size 0.2627 0.0485 ……. ……. 1.00 1- Write down the least square regression equation to predict the run time for run size. 2- Interpret the coefficients of the fitted model. 3- At 5% significance level, test if run size is a good…
5) What is true about a regression using data from a randomized controlled trial? a) The independent variable is exogenous because it was determined randomly. b) The line of best fit does not minimize the sum of squared residuals. c) It eliminates all error due to unmeasured variables. d) The estimated slope is significant no matter how many observations are in the sample. e) The slope of the line of best fit must be equal to the true relationship.
5
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 8096 probability? Round your answer to two decimal places (e.g. 98.76). Ancwor ic Rlanlk 1
4) In a univariate linear regression, explain intuitively, graphically and mathematically, how the variance of the estimated slope depends on a) the number of observations; b) the mean squared deviation of the independent variable; c) What else does it depend on? Can you explain how?
We have estimated the impact of gross domestic product (GDP), energy consumption (ENERGY) and population (POP) on CO2 emiisions (CO2) in Cyprus. The results are as follows; Dependent Variable: CO2 Method: Least Squares Date: 04/20/17 Time: 09:46 Sample: 1990 2013 Included observations: 24 Variable Coefficient Std. Error t-Statistic Prob. C 2.002813 6.458672 0.310097 0.7597 GDP 0.022114 0.011872 1.862670 0.0773 ENERGY -0.734352 0.328388 -2.236233 0.0369 POP 0.203927 0.293686 0.694371 0.4954 R-squared 0.825079 Mean dependent var 3.625982 Adjusted R-squared 0.798841 S.D. dependent var 0.108170 S.E. of regression 0.048515 Akaike info criterion -3.062883 Sum squared resid 0.047074 Schwarz criterion -2.866541 Log likelihood 40.75460 Hannan-Quinn criter. -3.010793 F-statistic 31.44583 Durbin-Watson stat 1.410912…
In reading the results of a multiple regression analysis that contained 4 predictor variables, the researcher noticed a column labeled Beta. Two of the Beta’s were positive and two were negative. He concluded that a.) Beta’s that were positive were statistically significant b.) Beta’s that were positive had more of an effect c.) Beta’s that were positive were associated with increases in the criterion variable d.) Beta’s that were positive did not affect the criterion because they were “controlled for…”
2. In building an arena, steel bars with a mean ultimate tensile strength of 400 Megapascal (MPa) with a variance of 81 MPa were delivered by the manufacturer. The project engineer tested 50 steel bars and found out that the mean ultimate tensile strength is 390 MPa. The decision for the extension of the contract with the manufacturer depends on the engineer. Test the hypothesis whether there is no significant difference between the two means using a two - tailed with a = 0.01.
The type of study that allows us to draw firm conclusions about the cause-and-effect relationship between two variables is a(n): a. experimental or quasi-experimental design b. experimental design c. correlational or quasi-experimental design d. correlational design
In a White test for heteroskedasticity, what is the degrees of freedom? The number of explanatory variables in the auxiliary regression + 1 The number of explanatory variables in the initial model + 1 The number of explanatory variables in the auxiliary regression The number of explanatory variables in the initial model

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