Q2. (a) Suppose that X B(n=10, p) and consider the point estimate. Let us consider =Xas12a point estimate of p.Xan unbiased point estimate of p? Justify your answer.12.i)Is p =-XWhat is the mean square error of p=12ii)b) Suppose that, E(X)= E(Y)= µ, Var(X)= 4, and Var(Y) = 6. What value of pminimizes the variance of u= pX +(2- p)Y? .Find the MSE of û.MAT361SSFinSp22.docx

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Answered: Q2. (a) Suppose that X ~ a point…

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 following table was generated from the sample data of 10 newborn babies regarding the weight of the mother at birth, the weight of the father at birth, and the weight of the baby at birth. The dependent variable is the weight of the baby, the first independent variable (x)) is the mother's weight, and the second independent variable (x2) is the father's weight. Coefficients Standard Error t-Stat p-value Intercept 9.739264 1.337045 7.284173 0.000165 Mother's Weight -0.929448 0.137340 - 6.767476 0.000261 Father's Weight 0.717791 0.159475 4.500951 0.002795 Copy Data Step 1 of 2: Write the multiple regression equation for the computer output given. Round your answers to three decimal places. Answer E Tables E Keypad How to enter your answer (opens in new window) Keyboard Shortcuts X + X2
A researcher collected data on ( X, Y ), and wanted to test if the true relationship is linear. Therefore, she collected replicated values of X. Here is a summary of the data, and some results: Xi No. of replicates yi SSE = 312. 1 3 9 10 5 11 8. 3 2 12 14 4 4. 15 13 3 9 6 6 5 11 10 7 1 8 4 8 3 7 5 At significance level a = 0.05, carry out the test of Lack-of-Fit for linearity of the model. No need to show an ANOVA Table. Calculations: Test statistic: T = Critical value = Conclusion: Since we 2.
In general, what is true about the relationship between the Sum of Squared Residuals in the restricted and unrestricted model? a. SSRr < SSRur b. SSRr > SSRur c. SSRr = SSRur d. SSRr = R-squared * SSRur
Let X ~ U(a,b). a Derive X mean and variance. b Use the method of moments to construct an estimator for a and for b. c Check whether those estimators are unbiased.
In the simple linear model Y = Bo + B1X+ ɛ, what is the interpretation of Betal_hat = 8.5? The point at which the line crosses the x-axis in 8.5 The point at which the line crosses the y-axis is 8.5 O The mean value of Y increases 8.5 units for every 1 unit increase X O The mean value of Y decreases 8.5 units for every 1 unit increase X
69 Q1. [6 points] :From the following data set 3\ 9. 1 6. 5. 4 11 16 1.find correlation coefficients 2. Estimate the simple linear regression model 3. Find the predicted value of y when x-10
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1) What is the slope(b1) and what is its statistical interpretation? 2) Perform the test of hypothesis (t-test) on the following and state your statistical decision. Use α = 0.01. Please show all the relevant calculations. H0: β1 = 0 H1: β1 ≠ 0 3) Perform the test of hypothesis (F-test) on the following and state your statistical decision. Use α = 0.01. Please show all the relevant calculations. H0: β1 = 0 H1: β1 ≠ 0 4) What is the coefficient of determination (r2) i.e., percentage of variability in the monthly rent explained by the independent variable rental property area? Please show all the relevant calculations. 5) What is the 99% confidence interval for the population slope(β1)? Please show all the relevant calculations.?
The built-in data set, rock, is a data frame recording the measurements of rock sample from a petroleum reservoir. We are interested in the area column of rock. Using R we can convert this column into the vector x by the assignment x<-rock$shape. Assume that the n area measurements x=(x1, x2,...,xn) are a random sample from a population with true unknown mean ? and true unknown variance ?2. Remember, let x be defined by x<-rock$shape.
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The prices of Rawlston, Inc. stock (y) over a period of 12 days, the number of shares (in 100s) of the company's stocks sold (x1), and the volume of exchange (in millions) on the New York Stock Exchange (x2) are shown below. 4. Perform an F test and determine whether independent variable and dependent variable are related. Fully interpret the meaning. Use α = .05 5. Conduct Residual Analysis and fully interpret the meaning. 6. If on a given day, the number of shares of the company that were sold was 94,500 and the volume of exchange on the New York Stock Exchange was 10 million, what would you expect the price of the stock to be? GRAPH IS SHOWN BELOW

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